Introduction to Mathematical Logic

Mendelson, E. (2015). Introduction to Mathematical Logic. CRC Press.

Type

Book

Intellectual base

Textbook

Year

2015

DOI

10.1201/b18519

ISBN

9780429162091

DOI registrant

Taylor & Francis (Chapman and Hall/CRC)

Link

https://doi.org/10.1201/b18519

Cited from

mathematics

Cited by

5 citations across 5 artifacts.

Each citation links to the sentence it supports in the citing article.

Primes

• Consistency
  • Mathematics and logic. An axiom set is consistent if no derivation from it yields both a formula and its negation; an inconsistent set trivializes the theory, since from a contradiction everything follows.

    This sourceStandard treatment of consistency of axiom sets and the derivation of all formulas from a contradiction.

Domain-specific

• Deductive closure
  • … constitutive identity and a convenient observable transfers from The deductive closure of axioms for a theory contains every theorem provable from those axioms in the chosen calculus. to Reasoning states whether consequence is semantic or syntactic and which logic and rules are in force before comparing closures..
• Formation rule
  • … between constitutive identity and a convenient observable transfers from If phi and psi are formulas, a rule may declare that open-parenthesis phi and psi close-parenthesis is also a formula. to A specification separates lexical, formation and inference rules and resolves precedence or ambiguity in concrete syntax..
• Literal (Mathematical Logic)
  • Standard accounts of formal syntax and satisfaction fix this boundary.
• Principle of distributivity
  • … between constitutive identity and a convenient observable transfers from A and (B or C) can be rewritten as (A and B) or (A and C) without changing any truth-table row. to Formula normalization tracks duplication cost and distinguishes classical equivalence from logics in which one or both distributive laws can fail..

Verification

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