Erik Palmgren

Denotational Semantics of Constraint Logic Programming — A Nonstandard Approach

NATO ASI Series, 1994

Groupoids and local cartesian closure

Locally cartesian closed categories without chosen constructions

Oavgörbara problem om ord och tal

logicism, intuitionism, and formalism - What has become of them?

... Finally, we wish to thank Professor Vincent Hendricks, Editor-in-Chief of Syn-these Library, ... more

A generalised cut characterisation of the axiom of fullness in CZF

Logic Journal of IGPL

Introduction: The Three Foundational Programmes

Logicism, Intuitionism, and Formalism, 2009

The period in the foundations of mathematics that started in 1879 with the publica-tion of Frege&... more

Introduction: The philosophy of logical consequence and inference

Synthese, 2012

There is a traditional picture of logic that may be spelled out roughly as follows: Logic is conc... more There is a traditional picture of logic that may be spelled out roughly as follows: Logic is concerned with the principles for correct reasoning and valid arguments; its principles are universal, necessary, a priori and formal; logically valid argument are necessarily truth-preserving and have a fundamental epistemic significance; and finally, logic is in some sense a normative discipline.

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Binary Refinement Implies Discrete Exponentiation

Studia Logica, 2007

Abstract. Working in the weakening of constructive Zermelo-Fraenkel set theory in which the subse... more

Logically Presented Domains

We connect the theory of Scott-Ershov domains to first order model theory. The completeness prope... more We connect the theory of Scott-Ershov domains to first order model theory. The completeness property of domains is related to the model theoretic notion of saturation. In constraint programming this analogy is already used on the level of finite approximations. A simple relation to structures used in nonstandard analysis (ultra powers, Frechet powers) is obtained. This leads to natural logical presentations of domain constructions such as function space, products and the Smyth power domain. Sufficient conditions on models for constructing function spaces are given

A categorical version of the BrouwerHeytingKolmogorov interpretation

Mathematical Structures in Computer Science, 2004

Double sequences, almost Cauchyness and BD-N

Logic Journal of IGPL, 2012

ABSTRACT

Denna C-kurs ger fordjupade kunskaper i logik och dess deduktiva och algoritmiska aspekter. Foljande moment ingar: Konstruktiv logik: Lambda-kalkyl och ML. Algoritmisk tolkning av de logiska konnektiven. Intuitionistisk logik. Martin-Lofs typteori. Programextraktion fran bevis. Integrerad pro- gr...

Quotient Spaces and Coequalisers in Formal Topology

Journal of Universal Computer Science, 2005

We give a construction of coequalisers in formal topology, a predicative ver- sion of locale theo... more

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Predicativity problems in point - free topology

CONTINUITY ON THE REAL LINE AND IN FORMAL SPACES

From Sets and Types to Topology and Analysis, 2005

From intuitionistic to point-free topology

Brouwer's pioneering results in topology, e. g. invariance of dimension, were devel-oped wit... more Brouwer's pioneering results in topology, e. g. invariance of dimension, were devel-oped within a classical framework of mathematics. Some years later he explained that "in his topological work he tried to use only methods which he expected could be made constructive" [11, p. XIV]. It seems that very little of algebraic topol-ogy, homotopy and homology, has actually been developed constructively in any detail, or, at any rate, found its way to publication. In the comprehensive treatise Foundations of Constructive Mathematics, Beeson [4, pp. 26-27] writes however

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A note on domain representability and formal topology

Two common approaches to constructive and effective topology are con- nected by showing that form... more

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Ramied Type Theory and Constructive Mathematics

Abstract. One hundred years ago Bertrand Russell published the first mature version of his type t... more Abstract. One hundred years ago Bertrand Russell published the first mature version of his type theory. It is a predicative but classical theory where the power sets are layered in an infinite sequence Pk(T) of ever more complete sets of subsets of a given type T. In this talk we show that a modernised intuitionistic version may be interpreted into Martin-L¨of type theory and used for development of constructive mathematics. The basic theory needs to be augmented with certain subset existence axioms to be useful. The fundamental one is the functional reducibility axiom which is a restricted and predicative version of Russell’s “infamous” reducibility axiom. It guarantees the existence of function spaces and real numbers. A further axiom that may be assumed is dependent choices. Both axioms may straightforwardly be interpreted in Martin-L¨of type theory. Adding W-types to the latter theory a scheme of generalized inductive definitions may be interpreted as well. All these axioms are ...

Category Theory and Structuralism

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