axiomatizable

Moreover, whilst Peano arithmetic is axiomatizable, there is a particular model of Peano arithmetic, whose theory is typically referred to as Number theory, which Godel demonstrated to be undecidable and non-axiomatizable.

Theories of Everything and Godel's theorem Gordon McCabe 2009

A theory is axiomatizable if there is a decidable set of sentences in the theory, whose closure under logical implication equals the entire theory.

Archive 2009-06-01 Gordon McCabe 2009

Moreover, whilst Peano arithmetic is axiomatizable, there is a particular model of Peano arithmetic, whose theory is typically referred to as Number theory, which Godel demonstrated to be undecidable and non-axiomatizable.

Archive 2009-06-01 Gordon McCabe 2009

A theory is axiomatizable if there is a decidable set of sentences in the theory, whose closure under logical implication equals the entire theory.

Theories of Everything and Godel's theorem Gordon McCabe 2009

There cannot be a single, recursively axiomatizable formal system for all of mathematics which is (a) consistent, (b) purely deductive, and (c) complete.

Non-Deductive Methods in Mathematics Baker, Alan 2009

The same author proved that a finite Łn is axiomatizable if it includes the theorems: CCpqCCqrCpr, CCCqrCCpqCpr,

Lvov-Warsaw School Wole&324;ski, Jan 2009

In fact, for many syntactical variants of PDL, their deterministic versions make up logics whose set of satisfiable formulas is not decidable or whose set of valid formulas is not axiomatizable.

Propositional Dynamic Logic Balbiani, Philippe 2007

Such is the case, e.g., of the first-order theory of torsion groups, known to be non-axiomatizable, and of incomplete modal logics which are only presented in syntactical (proof-theoretical) terms.

Combining Logics Carnielli, Walter 2007

Gödel's incompleteness theorems turn out to be generally applicable to all sufficiently strong but consistent recursively axiomatizable theories.

Philosophy of Mathematics Horsten, Leon 2007

Boolean algebras are traditionally defined axiomatically as complemented distributive lattices, which has the benefit of showing that they form a variety, and furthermore a finitely axiomatizable one.

Algebra Pratt, Vaughan 2007