An infinitary logic is a logic that allows infinitely long statements and/or infinitely long proofs. The concept was introduced by Zermelo in the 1930s...

mathematics and logic, an operation is finitary if it has finite arity, i.e. if it has a finite number of input values. Similarly, an infinitary operation is...

as its domain. Many extensions of first-order logic, including infinitary logics and higher-order logics, are more expressive in the sense that they do...

classical logics such as second-order logic or infinitary logic are also studied, along with Non-classical logics such as intuitionistic logic. First-order...

Formal logic Free logic Fuzzy logic Higher-order logic Infinitary logic Informal logic Intensional logic Intermediate logic Interpretability logic Intuitionistic...

proof trees or infinite derivation trees have also been studied, e.g. infinitary logic. Set theory is the branch of mathematics that studies sets, which are...

In mathematical logic, geometric logic is an infinitary generalisation of coherent logic, a restriction of first-order logic due to Skolem that is proof-theoretically...

In set theory, Ω-logic is an infinitary logic and deductive system proposed by W. Hugh Woodin (1999) as part of an attempt to generalize the theory of...

first-order logic.) Let L κ 2 {\displaystyle L_{\kappa }^{2}} be the infinitary logic for second-order set theory, permitting infinitary conjunctions...

Inductive logic -- Inductive logic programming -- Inference -- Inference procedure -- Inference rule -- Inferential role semantics -- Infinitary logic -- Infinite...

implication. In fact, a stronger claim is true: they must obey the infinitary logic Lω1,ω. We summarize these remarks as follows: The proposition system...

higher-order logics or infinitary logics is hampered by the fact that completeness and compactness do not in general hold for these logics. This is made...

In mathematics, ω-logic can refer to: ω-logic, an infinitary extension of first-order logic Ω-logic, a deductive system in set theory developed by Hugh...

least fixed point operator, and more generally for sentences in the infinitary logic L ∞ ω ω {\displaystyle L_{\infty \omega }^{\omega }} , which allows...

first-order logic. It thus applies to a very broad collection of logics, including first-order logic, higher-order logics, and infinitary logics. The Löwenheim...

(1985). Model-theoretic logics. Springer-Verlag. p. 295. ISBN 3-540-90936-2. Stanford Encyclopedia of Philosophy: "Infinitary Logic", Section 5, "Sublanguages...

data analysis. Fuzzy logic has made significant contributions in the fields of machine learning and data mining. In infinitary logic, degrees of provability...

In mathematics, infinitary combinatorics, or combinatorial set theory, is an extension of ideas in combinatorics to infinite sets. Some of the things studied...

van Heijenoort, 1967. From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931. Harvard Univ. Press. 1904. "Proof that every set can be well-ordered...

frame Predicate logic First-order logic Infinitary logic Many-sorted logic Higher-order logic Lindström quantifier Second-order logic Soundness theorem...

and the existence of nonisomorphic models equivalent in certain infinitary logics. In the meantime, many further applications have been found in Set...

to his discovery of the cumulative hierarchy and formalization of infinitary logic. The surprise with which set theorists met Skolem's paradox in the...

drawn from it. infinitary Pertaining to operations, languages, or logics that allow expressions of infinite length, such as infinitary logic. infinitesimal...

originally defined in terms of infinitary logic, where logical operators are allowed to take infinitely many operands. The logic on a regular cardinal κ is...

as part of logic. On the face of it, this damages the logicist programme also, albeit only for those already doubtful concerning 'infinitary methods'....

In deductive logic, a consistent theory is one that does not lead to a logical contradiction. A theory T {\displaystyle T} is consistent if there is no...

}}}}}}}},} where the left hand side uses Gauss's Kettenbruch notation. In infinitary logic, one can use infinite conjunctions and infinite disjunctions. Even...

extension to infinitary operations. Especially in order theory one finds numerous important variants of distributivity, some of which include infinitary operations...

category Law. Variations include multisorted (or multityped) Lawvere theory, infinitary Lawvere theory, and finite-product theory. Algebraic theory Clone (algebra)...

American mathematician of Dutch ancestry, best known for her work on infinitary logic. She also played viola in an all-women orchestra. Born in Michigan...