Alapfogalmak
Uniform preorders and triposes are closely related, with relationally complete uniform preorders corresponding to triposes with enough ∃-primes.
Kivonat
The content discusses the concept of uniform preorders, their relation to triposes, and the notion of relational completeness. It delves into the structure of uniform preorders, adjunctions, existential quantification, and indexed frames. The analysis highlights the equivalence between relationally complete uniform preorders and triposes with enough ∃-primes. Examples and propositions are provided to illustrate the concepts discussed.
Statisztikák
A uniform preorder is a pair (A, R) of a set A and a set R ⊆P(A × A) of binary relations on A.
A DCO is a set with a monoid of partial functions.
A uniform preorder is a set equipped with a monoid of binary relations.
A basis for a uniform preorder (A, R) is a subset R0 ⊆R of binary relations.
The locally ordered category UOrd of uniform preorders is characterized by a strict pullback of locally ordered categories.
Idézetek
"A central question remains open: every filtered OPCA gives rise to a relationally complete uniform preorder, but are there any others?"