Logic and Foundations

Typically, a logic consists of a formal or informal language together with a deductive system and/or a model-theoretic semantics.

Every set is smaller than its power set

In mathematics, specifically set theory, the continuum hypothesis (abbreviated CH) is a hypothesis

In the field of mathematical logic, a clear distinction is made between two notions of axioms: logical and non-logical.

it demonstrates a general technique that has since been used in a wide range of proofs, including the first of Godel's incompleteness theorems and Turing's answer to the Entscheidungsproblem.

The P = NP problem can also be stated as a question about expressive power in descriptive complexity.

Godel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories.

In computer science and mathematical logic the Turing degree (named after Alan Turing) or degree of unsolvability of a set of natu

nt consistency theorem is an important theorem of mathematical logic.

In mathematical logic, a theory is categorical if it has exactly one model (up to isomorphism).

In mathematical logic and computer science, Gabbay's separation theorem states that any formula in linear temporal logic (LTL) wit

In mathematical logic, a deduction theorem is a metatheorem that justifies doing conditional proofs from a hypothesis in systems t

In mathematical logic, a theory can be extended with new constants or function names under certain conditions with assurance that

In modal logic, Sahlqvist formulas are a certain kind of modal formula with remarkable properties.

In logic, soundness can refer to either a property of arguments or a property of formal deductive systems.

In logic, mathematics, and computer science, arity ( ) is the number of arguments or operands taken by a function, operation or re

In logic, negation, also called the logical not or logical complement, is an operation that takes a proposition P to another propo

In mathematical logic, a sequent is a very general kind of conditional assertion.

In quantified modal logic, the Barcan formula and the converse Barcan formula (more accurately, schemata rather than formulas) (i)

In mathematical logic, Craig's interpolation theorem is a result about the relationship between different logical theories.

In mathematical logic, the Beth definability theorem is a fundamental result in logic that states a property implicitly defined by

In mathematical logic, an omega-categorical theory is a theory that has exactly one countably infinite model up to isomorphism.

In mathematical logic, a formula is said to be absolute to some class of structures (also called models), if it has the same truth

ph property definable in the monadic second-order logic of graphs can be decided in linear time on graphs of bounded treewidth.

In mathematical logic, the diagonal lemma (also known as diagonalization lemma, self-reference lemma or fixed point theorem) estab

In metalogic and metamathematics, Frege's theorem is a metatheorem that states that the Peano axioms of arithmetic can be derived

In mathematical logic, the Barwise compactness theorem, named after Jon Barwise, is a generalization of the usual compactness theo

In mathematical logic and computer science, Kamp's theorem states that linear temporal logic is equivalent to the monadic first-or

In mathematical logic, Goodstein's theorem is a statement about the natural numbers, proved by Reuben Goodstein in 1944, which sta

who presented the theorem in 1959, is a result in mathematical logic that states that no countable nonstandard model of first-orde

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