Search results

...in [[classical logic]], this means that for every [[Sentence (mathematical logic)|sentence]], the theory contains either the sentence or its negation but no ...signature (logic)|signature]] ''σ'' is [[κ-categorical|<math>\kappa</math>-categorical]] for an [[infinite cardinal]] <math>\kappa</math> if <math>T</math> has ex ...

{{short description|Mathematical logic theory with exactly one countably infinite model up to isomorphism}} ...-categorical'''. The notion is most important for countable [[first-order logic|first-order]] theories. ...

...elieved this principle was a [[Categorical imperative#Freedom and autonomy|categorical freedom]], bound only by the [[free will]] as opposed to the [[David Hume|H ...ormed under the assumption of different conditions on different [[Temporal logic#Motivation|branches of timelines]] in the future, and past obligation assig ...

In [[model theory]], a branch of [[mathematical logic]], the '''Hrushovski construction''' generalizes the [[Age (model theory)|F ...dental.<ref name=pseudoplane>E. Hrushovski. A stable <math>\aleph_0</math>-categorical pseudoplane. ''Preprint, 1988''</ref> ...

...wvere]]) is a [[category (mathematics)|category]] that can be considered a categorical counterpart of the notion of an [[equational theory]]. ...Theoretical Computer Science |volume=172 |issue=Computation, Meaning, and Logic: Articles dedicated to Gordon Plotkin |pages=437–458 |doi=10.1016/j.entcs.2 ...

In [[type theory]], a discipline within mathematical logic, '''containers''' are abstractions which permit various "collection types", == Categorical aspects == ...

...al category has a terminal object. The scone category inherits almost any categorical construct the original category has. Scones can be used to generally descr ...t2=Scott |first2=Philip J. |title=Introduction to higher order categorical logic |date=1994 |publisher=Cambridge Univ. Press |location=Cambridge |isbn=97805 ...

...tegory-theoretic analog to the logical concept of a [[Theory (mathematical logic)|theory]] and its [[Model theory|models]]. They allow multisorted models an | title = Handbook of Categorical Algebra. 2. Categories and Structures ...

In [[model theory]], a discipline within the field of [[mathematical logic]], a '''tame abstract elementary class''' is an [[abstract elementary class ...laim 2.3 (9.2 in the online version).</ref> If an AEC with amalgamation is categorical in a cardinal <math>\lambda</math> of high-enough cofinality, then tameness ...

The categorical point of view is useful since by [[Yoneda's lemma]], a generalized metric s * {{cite journal |doi=10.1007/BF02924844 |title=Metric spaces, generalized logic, and closed categories |date=1973 |last1=Lawvere |first1=F. William |journa ...

In [[mathematical logic]] and [[metalogic]], a [[formal system]] is called '''complete''' with resp ...on the context, mostly referring to the property of semantical [[Validity (logic)|validity]]. Intuitively, a system is called complete in this particular se ...

'''Logic learning machine''' ('''LLM''') is a [[machine learning]] method based on t | title=Use of Attribute Driven Incremental Discretization and Logic Learning Machine to build a prognostic classifier for neuroblastoma patient ...

...an [[elementary substructure]] of an [[elementary class]] in [[first-order logic|first-order]] model theory. They were introduced by [[Saharon Shelah]].<ref ...1, \omega}</math>, and <math>\mathcal{F}</math> is a countable [[fragment (logic)|fragment]] containing <math>\phi</math>, then <math> \langle \operatorname ...

...proof of [[Omega-categorical theory|equivalent characterizations of omega-categorical theories]]. A 1959 paper of his in ''[[Theoria (philosophy journal)|Theoria Lars Svenonius' early work was in the field of logic known as model theory, in which properties of the interpretations ("models" ...

...S. Shapiro, ''Foundations Without Foundationalism: A Case for Second-order Logic'' (1991).</ref> ...=2009.07164 |author1=Joel David Hamkins |author2=Hans Robin Solberg |title=Categorical large cardinals and the tension between categoricity and set-theoretic refl ...

{{distinguish|Interpretation (logic)}} ...]] ''M'' in another structure ''N'' (typically of a different [[signature (logic)|signature]]) is a technical notion that approximates the idea of represent ...

{{Short description|Method in mathematical logic}} ...ion''') is a method used to construct (infinite) [[Structure (mathematical logic)|mathematical structures]] from their (finite) [[Substructure (mathematics) ...

In [[mathematical logic]], [[category theory]], and == Categorical semantics == ...

In [[theoretical computer science]] and [[mathematical logic]], '''assemblies''' can be informally described as sets equipped with repre Assemblies are equipped with a [[category (mathematics)|categorical]] structure as follows. A morphism <math>f : S \to T</math> between assembl ...

...edge representation |series=[[Synthese]] library: studies in epistemology, logic, methodology, and philosophy of science |volume=359 |location=Cham |publish ...edge representation |series=[[Synthese]] library: studies in epistemology, logic, methodology, and philosophy of science |volume=359 |location=Cham |publish ...