scientific article

Publication date: 1979

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

types quotients internalization category of sheaves sheaf topoi complete Heyting algebras as generalized topologies internal reals interpretation of first-order logic interpretation of higher-order logic interpretation of logic in categories of sheaves sheaves over complete Heyting algebras

Mathematics Subject Classification ID

Topological spaces and generalizations (closure spaces, etc.) (54A05) Categorical logic, topoi (03G30) Heyting algebras (lattice-theoretic aspects) (06D20) Topoi (18B25) Nonclassical models (Boolean-valued, sheaf, etc.) (03C90)

Related Items

Remarks on the tripos to topos construction: comprehension, extensionality, quotients and functional-completeness, Sheaves over Heyting lattices, Quasitopoi, logic and Heyting-valued models, Some corollaries of the correspondence between partial metrics and multivalued equalities, Sheaves on involutive quantales: Grothendieck quantales., Quantale-valued preorders: globalization and cocompleteness., Transfer from deducibility in the classical set theory to deducibility in intuitionistic set theory for the language of rings, Lindenbaum algebras of intuitionistic theories and free categories, \(\mathcal Q\)-\(*\)-categories, A sheaf model for intuitionistic quantum mechanics, Embedding sheaf models for set theory into Boolean-valued permutation models with an interior operator, Generalized algebraic theories and contextual categories, Logic in Category Theory, The logical quantization of algebraic groups, Well-foundedness in realizability, Degrees of Unsolvability: A Tutorial, Universes of fuzzy sets and axiomatizations of fuzzy set theory. II: Category theoretic approaches, Some connections between Heyting valued set theory and algebraic geometry. Prolegomena to intuitionistic algebraic geometry, Conceptual completeness for first-order intuitionistic logic: An application of categorical logic, Quotients with respect to similarity relations, Is the category JTF a topos?, Diego's theorem for nuclear implicative semilattices, Quantum set theory: transfer principle and De Morgan's laws, Classifying toposes for first-order theories, Generalized logic and the representation of rings, Fuzzy sets and sheaves. I: Basic concepts, Fuzzy sets and sheaves. II: Sheaf-theoretic foundations of fuzzy set theory with applications to algebra and topology, \(E\)-fuzzy groups, Syntax and semantics of the logic \({\mathcal L}_{\omega\omega}^\lambda\), On Tarski’s fixed point theorem, Liminf convergence in \(\Omega\)-categories, Fibrations and recursivity, Isomorphisms and functors of fuzzy sets and cut systems, Completions of cut systems in \(Q\)-sets, Topological forcing semantics with settling, The order-theoretic duality and relations between partial metrics and local equalities, ORTHOMODULAR-VALUED MODELS FOR QUANTUM SET THEORY, Preordered sets valued in a GL-monoid, Cut approach to invariance groups of lattice-valued functions, Many-Valued Preorders II: The Symmetry Axiom and Probabilistic Geometry, Tameness in generalized metric structures, Topological inductive definitions, Categories, toposes and sets, Solving linear equations by fuzzy quasigroups techniques, Elementary inductive definitions in HA: From strictly positive towards monotone, The number of countable models in realizability toposes, The universe of discourse of modal logic, Quantale-valued dissimilarity, The logic of approximation in quantum theory, Sheaves on sites as Cauchy-complete categories, The World's simplest axiom of choice fails, Fuzzy sets in topoi, Fuzzy sets do not form a topos, A survey of fuzzy set and topos theory, Groupoid sheaves as quantale sheaves, Three Lessons on the Topological and Algebraic Hidden Core of Rough Set Theory, A semantic hierarchy for intuitionistic logic, Generalising the étale groupoid-complete pseudogroup correspondence, Constructive \(\lambda\)-models, R n - and G n -logics, Unnamed Item, Unnamed Item, Unnamed Item, A non-commutative and non-idempotent theory of quantale sets, Fuzzy presubsets as non-idempotent and non-commutative classifications of subalgebras, Quadratic form theory over preordered von Neumann-regular rings, TOPOLOGY AND MODALITY: THE TOPOLOGICAL INTERPRETATION OF FIRST-ORDER MODAL LOGIC, A natural interpretation of fuzzy sets and fuzzy relations, When does a category built on a lattice with a monoidal structure have a monoidal structure?, Sheaves as modules, Topological aspects of non-convergent sequences -- a comment on Burgin's concept of fuzzy limits, \(\Omega\)-lattices, Monadic bounded algebras, Cubical Type Theory: a constructive interpretation of the univalence axiom, Weak logic theory, Foundations of fuzzy sets, Positive definite functions over regular f-rings and representations as sums of squares, L-equivalence relations on L-fuzzy sets, L-partitions of L-fuzzy sets and their one-to-one connections, \( \Omega \)-groups in the language of \(\Omega \)-groupoids, On principally generated quantaloid-modules in general, and skew local homeomorphisms in particular, A new model for intuitionistic analysis, A semantical proof of De Jongh's theorem, Notions of computation and monads, Neighborhood-Sheaf Semantics for First-Order Modal Logic, Global intuitionistic analysis, Topoi and categories of fuzzy sets, A study on the relationship between relaxed metrics and indistinguishability operators, Sheaf models and massless fields, Some purely topological models for intuitionistic analysis, Completion of L-fuzzy relations, Boolean combinations of monadic formulas, On the collection of points of a formal space, Sheaf models for choice sequences, On some non-classical extensions of second-order intuitionistic propositional calculus, Implementing Local Intervals in CASL, Proper maps of locales, Monoidal closed categories, weak topoi and generalized logics, The lack of definable witnesses and provably recursive functions in intuitionistic set theories, Arithmetic transfinite induction and recursive well-orderings, Mathematical aspects of fuzzy sets and fuzzy logic. Some reflections after 40 years, Normal Ω-subgroups, Diagonals between \(\mathcal{Q}\)-distributors, Omega-rings, Solutions of matrix equations with weak fuzzy equivalence relations, Unnamed Item, SEPARATING THE FAN THEOREM AND ITS WEAKENINGS II, Ω-lattices from skew lattices, QUANTIFIED INTUITIONISTIC LOGIC OVER METRIZABLE SPACES, Aspects of Categorical Recursion Theory