aquatic
发表于 2025-3-28 14:34:37
Categories,verviewof the categorical concepts and results used by this book. The reader without enough familiarity with category theory is advised to use one of the textbooks on category theory available in the literature. and are among standard references for category theory. A reference for indexe
Abbreviate
发表于 2025-3-28 20:54:15
Institutions,relation between models and sentences with respect to the change of notation. This is our first example of an institution. We then introduce the abstract concept of institution and illustrate it by a list of examples from logic and computing science. The next section introduces morphisms and comorph
CIS
发表于 2025-3-29 00:57:03
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insert
发表于 2025-3-29 05:02:50
Model Ultraproducts,lying upon ‘first order’ quantifiers (handled by representable signature morphisms) and finiteness at various syntactic levels such as arities of symbols, atoms, quantification, and logical connectives.
paradigm
发表于 2025-3-29 07:13:18
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Delectable
发表于 2025-3-29 13:33:53
Preservation and Axiomatizability, theories in purely semantic terms, formulated as closure properties of classes of models under some categorical operators. Perhaps the most famous example is the Birkhoff Variety theorem of equational logic: a class of algebras for a signature is closed under products, sub-algebras, and homomorphic
谷类
发表于 2025-3-29 17:38:49
Interpolation, in . (propositional logic): . where ., ., . are propositional symbols (i.e., relation symbols of zero arity). The simplest justification for this deduction is by factoring it as . which meets the intuition that . is not involved in establishing the truth of . ∨ .. In general, the so-called ‘Craig i
黑豹
发表于 2025-3-29 23:13:31
Possible Worlds,nd ‘possibility’. While at the sentence level this means a couple of additional unary connectives (□ for ‘necessity” and ⋄ for ‘possibility’), their semantics is much less straightforward because it requires the concept of ‘possible worlds’ semantics, which means that the models are Kripke models, i
patella
发表于 2025-3-30 00:52:00
Grothendieck Institutions,egarded from a fibration theoretic angle, Grothendieck institutions are just institutions for which their category of signatures is fibred. For example, the actual institutions with many-sorted signatures appear naturally as fibred institutions determined by the fibrations given by the functor mappi
TOXIN
发表于 2025-3-30 05:19:58
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