Open Logic Project Builds: Portuguese

This site contains PDFs built from the source LaTeX files of the most recent version of the Open Logic Text in Portuguese.

Complete PDFs

We have PDFs of the complete text in the Open Logic (Portuguese) main branch, arranged in a somewhat sensible manner, including editorial comments. It's not intended as a textbook, but it shows what's there.

• Open Logic Text, Complete Clean Version: one big PDF of all the material, without extra markup.
• Open Logic Text, Complete Debug Version: one big PDF with additional markup to identify source files and OLT-specific commands.

Individual Textbooks

There are already a few textbooks that show how one might "remix" the material in the Open Logic Project to produce nice textbooks. These vary in the material that's included, the design, and the configuration options used. They may also include additional material specific to those courses.

Conjuntos, Lógica, Computação (Sets, Logic, Computation)

A textbook on metalogic, developed for Calgary's Logic II course: includes the material on set theory, first-order logic (including both sequent calculus and natural deduction), and Turing machines (including undecidability). Appendices cover proofs and induction and biographies of some logicians. This text also includes chapter summaries and a glossary. Problems are collected at the end of chapters.

• slc-screen.pdf for screen reading (color, smaller margins, low-res images)
• slc-print.pdf for print-on-demand (without cover)

Teoria dos Conjuntos (Set Theory)

A brief introduction to the philosophy of set theory; covers why set theory came about; how to reduce large swathes of mathematics to set theory + arithmetic; how to embed arithmetic in set theory; what the cumulative iterative conception of set amounts to; how one might try to justify the axioms of ZFC. Most of the material making up the text comes from Tim Button's Open Set Theory.

• settheory-screen.pdf for screen reading (color, smaller margins, low-res images)
• settheory-print.pdf for print-on-demand (without cover)

Parts, Chapters, Sections

1. sets-functions-relations-complete
   1. sets
      1. basics
      2. subsets
      3. important-sets
      4. unions-and-intersections
      5. pairs-and-products
      6. russells-paradox
   2. relations-complete
      1. relations-as-sets
      2. reflections
      3. special-properties
      4. equivalence-relations
      5. orders
      6. graphs
      7. trees
      8. operations
   3. functions
      1. function-basics
      2. function-kinds
      3. functions-relations
      4. inverses
      5. composition
      6. isomorphic-functions
      7. partial-functions
   4. size-of-sets-complete
      1. introduction
      2. enumerability
      3. zig-zag
      4. pairing
      5. pairing-alt
      6. non-enumerability
      7. reduction
      8. equinumerous-sets
      9. comparing-size
      10. schroder-bernstein
      11. enumerability-alt
      12. non-enumerability-alt
      13. reduction-alt
   5. arithmetization
      1. integers
      2. rationals
      3. reals
      4. cuts
      5. reflections
      6. checking-details
      7. cauchy
   6. infinite
      1. hilberts-hotel
      2. dedekind-algebra
      3. dedekind-induction
      4. dedekinds-proof
      5. card-sb
2. propositional-logic
   1. syntax-and-semantics
      1. introduction
      2. formulas
      3. preliminaries
      4. formation-sequences
      5. valuations-sat
      6. semantic-notions
3. first-order-logic
   1. introduction
      1. first-order-logic
      2. syntax
      3. formulas
      4. satisfaction
      5. sentences
      6. semantic-notions
      7. substitution
      8. models-theories
      9. soundness-completeness
   2. syntax
      1. intro-syntax
      2. first-order-languages
      3. terms-formulas
      4. unique-readability
      5. main-operator
      6. subformulas
      7. formation-sequences
      8. free-vars-sentences
      9. substitution
   3. semantics
      1. intro-semantics
      2. structures
      3. covered-structures
      4. satisfaction
      5. assignments
      6. extensionality
      7. semantic-notions
   4. models-theories
      1. introduction
      2. expressing-props-of-structures
      3. theories
      4. expressing-relations
      5. set-theory
      6. size-of-structures
   5. proof-systems
      1. introduction
      2. sequent-calculus
      3. natural-deduction
      4. tableaux
      5. axiomatic-deduction
   6. sequent-calculus
      1. rules-and-proofs
      2. propositional-rules
      3. quantifier-rules
      4. structural-rules
      5. derivations
      6. proving-things
      7. proving-things-quant
      8. proof-theoretic-notions
      9. provability-consistency
      10. provability-propositional
      11. provability-quantifiers
      12. soundness
      13. identity
      14. soundness-identity
   7. natural-deduction
      1. rules-and-proofs
      2. propositional-rules
      3. quantifier-rules
      4. derivations
      5. proving-things
      6. proving-things-quant
      7. proof-theoretic-notions
      8. provability-consistency
      9. provability-propositional
      10. provability-quantifiers
      11. soundness
      12. identity
      13. soundness-identity
   8. tableaux
      1. rules-and-proofs
      2. propositional-rules
      3. quantifier-rules
      4. derivations
      5. proving-things
      6. proving-things-quant
      7. proof-theoretic-notions
      8. provability-consistency
      9. provability-propositional
      10. provability-quantifiers
      11. soundness
      12. identity
      13. soundness-identity
   9. axiomatic-deduction
      1. rules-and-proofs
      2. axioms-rules-propositional
      3. axioms-rules-quantifiers
      4. proving-things
      5. proving-things-quant
      6. proof-theoretic-notions
      7. deduction-theorem
      8. deduction-theorem-quantifiers
      9. provability-consistency
      10. provability-propositional
      11. provability-quantifiers
      12. soundness
      13. identity
   10. completeness
       1. introduction
       2. outline
       3. complete-consistent-sets
       4. henkin-expansions
       5. lindenbaums-lemma
       6. construction-of-model
       7. identity
       8. completeness-thm
       9. compactness
       10. compactness-direct
       11. downward-ls
   11. beyond
       1. introduction
       2. many-sorted-logic
       3. second-order-logic
       4. higher-order-logic
       5. intuitionistic-logic
       6. modal-logics
       7. other-logics
4. model-theory
   1. basics
      1. reducts-and-expansions
      2. substructures
      3. overspill
      4. isomorphism
      5. theory-of-m
      6. partial-iso
      7. dlo
      8. nonstandard-arithmetic
   2. models-of-arithmetic
      1. introduction
      2. standard-models
      3. non-standard-models
      4. models-of-q
      5. models-of-pa
      6. computable-models
   3. interpolation
      1. introduction
      2. separation
      3. interpolation-proof
      4. definability
   4. lindstrom
      1. introduction
      2. abstract-logics
      3. ls-property
      4. lindstrom-proof
5. computability
   1. recursive-functions
      1. introduction
      2. primitive-recursion
      3. composition
      4. pr-functions
      5. notation-pr-functions
      6. pr-functions-computable
      7. examples
      8. pr-relations
      9. bounded-minimization
      10. primes
      11. sequences
      12. trees
      13. other-recursions
      14. non-pr-functions
      15. partial-functions
      16. normal-form
      17. halting-problem
      18. general-recursive-functions
   2. computability-theory
      1. introduction
      2. coding-computations
      3. normal-form
      4. s-m-n
      5. universal-part-function
      6. no-universal-function
      7. halting-problem
      8. russells-paradox
      9. computable-sets
      10. ce-sets
      11. equiv-ce-defs
      12. non-comp-set
      13. ce-closed-cup-cap
      14. complement-ce
      15. reducibility
      16. prop-reduce
      17. complete-ce-sets
      18. k-1
      19. total
      20. rice-theorem
      21. fixed-point-thm
      22. application-fixed-point
      23. def-functions-self-reference
6. turing-machines
   1. machines-computations
      1. introduction
      2. representing-tms
      3. turing-machines
      4. configuration
      5. unary-numbers
      6. halting-states
      7. disciplined-machines
      8. combining-machines
      9. variants
      10. church-turing-thesis
   2. undecidability
      1. introduction
      2. enumerating-tms
      3. universal-tm
      4. halting-problem
      5. decision-problem
      6. representing-tms
      7. verification
      8. unsolvability-decision-problem
      9. trakhtenbrot
7. incompleteness
   1. introduction
      1. historical-background
      2. definitions
      3. overview
      4. undecidability
   2. arithmetization-syntax
      1. introduction
      2. coding-symbols
      3. coding-terms
      4. coding-formulas
      5. substitution
      6. proofs-in-lk
      7. proofs-in-nd
      8. proofs-in-ax
   3. representability-in-q
      1. introduction
      2. representable-comp
      3. beta-function
      4. prim-rec
      5. basic-representable
      6. composition-representable
      7. minimization-representable
      8. comp-representable
      9. representing-relations
      10. undecidability
      11. sigma1-completeness
   4. theories-computability
      1. introduction
      2. q-is-ce
      3. oconsis-ext-of-q-undec
      4. extensions-of-q-not-decidable
      5. computably-axiomatizable
      6. complete-decidable
      7. first-incompleteness
      8. inseparability
      9. consis-with-q
      10. interpretability
   5. incompleteness-provability
      1. introduction
      2. fixed-point-lemma
      3. first-incompleteness-thm
      4. rosser-thm
      5. godels-paper
      6. provability-conditions
      7. second-incompleteness-thm
      8. lob-thm
      9. tarski-thm
8. second-order-logic
   1. syntax-and-semantics
      1. introduction
      2. terms-formulas
      3. satisfaction
      4. semantic-notions
      5. expressive-power
      6. inf-count
   2. metatheory
      1. introduction
      2. second-order-arithmetic
      3. undecidability-and-axiomatizability
      4. compactness
      5. loewenheim-skolem
   3. sol-and-set-theory
      1. introduction
      2. comparing-sets
      3. cardinalities
      4. power-of-continuum
9. lambda-calculus
   1. introduction
      1. overview
      2. syntax
      3. reduction
      4. church-rosser
      5. currying
      6. lambda-definability
      7. lambda-computable
      8. computable-lambda
      9. basic-pr-lambda
      10. composition
      11. primitive-recursion
      12. fixed-point-combinator
      13. minimization
   2. syntax
      1. terms
      2. unique-readability
      3. abbreviated-syntax
      4. free-variables
      5. substitution
      6. alpha
      7. de-bruijn
      8. term-revisited
      9. beta
      10. eta
   3. church-rosser
      1. definitions-and-properties
      2. parallel-beta-reduction
      3. beta-reduction
      4. parallel-beta-eta-reduction
      5. beta-eta-reduction
   4. lambda-definability
      1. introduction
      2. arithmetical-functions
      3. pairs
      4. truth-values
      5. lists
      6. primitive-recursive-functions
      7. fixpoints
      8. minimization
      9. partial-recursive-functions
      10. lambda-definable-recursive
10. many-valued-logic
    1. syntax-and-semantics
       1. introduction
       2. connectives
       3. formulas
       4. matrices
       5. valuations-sat
       6. semantic-notions
       7. sublogics
    2. three-valued-logics
       1. introduction
       2. lukasiewicz
       3. kleene
       4. goedel
       5. multiple-designation
    3. infinite-valued-logics
       1. introduction
       2. lukasiewicz
       3. goedel
    4. sequent-calculus
       1. introduction
       2. rules-and-proofs
       3. structural-rules
       4. propositional-rules
11. normal-modal-logic
    1. syntax-and-semantics
       1. introduction
       2. language-modal-logic
       3. substitution
       4. relational-models
       5. truth-at-w
       6. truth-in-model
       7. modal-validity
       8. tautological-instances
       9. schemas
       10. entailment
    2. frame-definability
       1. introduction
       2. properties-accessibility
       3. frames
       4. definability
       5. first-order-definability
       6. equivalence-S5
       7. second-order-definability
    3. axioms-systems
       1. introduction
       2. normal-logics
       3. logics-proofs
       4. proofs-in-K
       5. derived-rules
       6. more-proofs-in-K
       7. duals
       8. proofs-modal-systems
       9. soundness
       10. systems-distinct
       11. provability-from-set
       12. provability-properties
       13. consistency
    4. completeness
       1. introduction
       2. complete-consistent-sets
       3. lindenbaums-lemma
       4. modalities-ccs
       5. canonical-models
       6. truth-lemma
       7. completeness-K
       8. frame-completeness
    5. filtrations
       1. introduction
       2. preliminaries
       3. filtrations-def
       4. examples-of-filtrations
       5. finite
       6. S5-fmp
       7. S5-decidable
       8. more-filtrations
       9. euclidean-filtrations
    6. tableaux
       1. introduction
       2. rules-for-K
       3. proofs-in-K
       4. soundness
       5. more-rules
       6. more-soundness
       7. simple-S5
       8. completeness
       9. countermodels
    7. sequent-calculus
       1. introduction
       2. rules-for-K
       3. proofs-in-K
       4. soundness
       5. more-rules
       6. more-soundness
       7. hypersequents-S5
12. applied-modal-logic
    1. temporal-logic
       1. introduction
       2. temporal-logic-semantics
       3. properties-accessibility
       4. extra-temporal-operators
       5. possible-histories
    2. epistemic-logic
       1. introduction
       2. language-epistemic-logic
       3. relational-models
       4. truth-at-w
       5. properties-accessibility
       6. bisimulations
       7. public-announcement-logic-lang
       8. public-announcement-logic-semantics
13. intuitionistic-logic
    1. introduction
       1. constructive-reasoning
       2. syntax
       3. bhk-interpretation
       4. natural-deduction
       5. axiomatic-derivations
    2. semantics
       1. introduction
       2. relational-models
       3. semantic-notions
       4. topological-semantics
    3. soundness-completeness
       1. soundness-axd
       2. soundness-nd
       3. lindenbaum
       4. canonical-model
       5. truth-lemma
       6. completeness-thm
       7. decidability
    4. tableaux
       1. introduction
       2. rules
       3. proofs
       4. soundness
       5. completeness
       6. countermodels
    5. propositions-as-types
       1. introduction
       2. sequent-natural-deduction
       3. proof-terms
       4. proofs-to-terms
       5. terms-to-proofs
       6. reduction
       7. normalization
14. counterfactuals
    1. introduction
       1. material-conditional
       2. paradoxes-material
       3. strict-conditional
       4. counterfactuals
    2. minimal-change-semantics
       1. introduction
       2. sphere-models
       3. true-false
       4. antecedent-strengthening
       5. transitivity
       6. contraposition
15. set-theory
    1. story
       1. extensionality
       2. russells-paradox-again
       3. predicativity
       4. cumulative-approach
       5. urelements
       6. grundgesetze
    2. z
       1. story
       2. separation
       3. union
       4. pairs
       5. powerset
       6. infinity-again
       7. milestone
       8. nat
       9. arbintersections
    3. ordinals
       1. introduction
       2. idea
       3. wo
       4. iso
       5. vn
       6. basic
       7. replacement
       8. milestone
       9. ordtype
       10. opps
    4. spine
       1. idea
       2. recursion
       3. stagesbasics
       4. foundation
       5. zf
       6. rank
    5. replacement
       1. introduction
       2. strength
       3. extrinsic
       4. limofsize
       5. absinf
       6. ref
       7. refproofs
       8. finiteaxiomatizability
    6. ord-arithmetic
       1. introduction
       2. addition
       3. using-addition
       4. multiplication
       5. exponentiation
    7. cardinals
       1. cp
       2. cardsasords
       3. milestone
       4. classing
       5. hp
    8. card-arithmetic
       1. opps
       2. simp
       3. expotough
       4. ch
       5. fix
    9. choice
       1. introduction
       2. tarskiscott
       3. hartogs
       4. wellorderingproblem
       5. countablechoice
       6. justifications
       7. banach
       8. vitali
16. methods
    1. proofs
       1. introduction
       2. starting-proofs
       3. using-definitions
       4. inference-patterns
       5. example-1
       6. example-2
       7. proof-by-contradiction
       8. reading-proofs
       9. cant-do-it
       10. resources
    2. induction
       1. introduction
       2. induction-on-N
       3. strong-induction
       4. inductive-definitions
       5. structural-induction
       6. relations
17. history
    1. biographies
       1. georg-cantor
       2. alonzo-church
       3. gerhard-gentzen
       4. kurt-goedel
       5. emmy-noether
       6. rozsa-peter
       7. julia-robinson
       8. bertrand-russell
       9. alfred-tarski
       10. alan-turing
       11. ernst-zermelo
    2. set-theory
       1. infinitesimals
       2. limits
       3. pathologies
       4. mythology
       5. cantor-plane
       6. hilbert-curve
18. reference
    1. greek-alphabet
    2. fraktur-alphabet

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