Basic Operations on Preordered Coherent Spaces

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Basic Operations on Preordered Coherent Spaces

This Mizar paper presents the definition of a "Preordered Coherent Space" (PCS). Furthermore, the paper defines a number of operations on PCS's and states and proves a number of elementary lemmas about these operations. PCS's have many useful properties which could qualify them for mathematical study in their own right. PCS's were invented, however, to construct Scott domains, to solve domain equations, and to construct models of various versions of lambda calculus.

For more on PCS's, see [11]. The present Mizar paper defines the operations on PCS's used in Chapter 8 of [3].

[1] Grzegorz Bancerek. König's theorem. Formalized Mathematics, 1(3):589-593, 1990.

[2] Grzegorz Bancerek. The "way-below" relation. Formalized Mathematics, 6(1):169-176, 1997.

[3] Chantal Berline and Klaus Grue. A kappa-denotational semantics for map theory in ZFC + SI. Theoretical Computer Science, 179(1-2):137-202, 1997.

[4] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.

[5] Czesław Byliński. The modification of a function by a function and the iteration of the composition of a function. Formalized Mathematics, 1(3):521-527, 1990.

[6] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.

[7] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.

[8] Adam Grabowski and Robert Milewski. Boolean posets, posets under inclusion and products of relational structures. Formalized Mathematics, 6(1):117-121, 1997.

[9] Zbigniew Karno. Separated and weakly separated subspaces of topological spaces. Formalized Mathematics, 2(5):665-674, 1991.

[10] Artur Korniłowicz. Cartesian products of relations and relational structures. Formalized Mathematics, 6(1):145-152, 1997.

[11] J.L. Krivine. Lambda-calculus, types and models. Ellis & Horwood, 1993.

[12] Beata Madras. Product of family of universal algebras. Formalized Mathematics, 4(1):103-108, 1993.

[13] Markus Moschner. Basic notions and properties of orthoposets. Formalized Mathematics, 11(2):201-210, 2003.

[14] Konrad Raczkowski and Paweł Sadowski. Equivalence relations and classes of abstraction. Formalized Mathematics, 1(3):441-444, 1990.

[15] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1):115-122, 1990.

[16] Andrzej Trybulec. Tarski Grothendieck set theory. Formalized Mathematics, 1(1):9-11, 1990.

[17] Andrzej Trybulec. Tuples, projections and Cartesian products. Formalized Mathematics, 1(1):97-105, 1990.

[18] Andrzej Trybulec. Many-sorted sets. Formalized Mathematics, 4(1):15-22, 1993.

[19] Wojciech A. Trybulec and Grzegorz Bancerek. Kuratowski - Zorn lemma. Formalized Mathematics, 1(2):387-393, 1990.

[20] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.

[21] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.

[22] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.

[23] Edmund Woronowicz and Anna Zalewska. Properties of binary relations. Formalized Mathematics, 1(1):85-89, 1990.

Formalized Mathematics

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Journal Information

SCImago Journal Rank (SJR) 2016: 0.207
Source Normalized Impact per Paper (SNIP) 2016: 0.315

Target Group

researchers in the fields of formal methods and computer-checked mathematics


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