On the number of types
| Autor: | Miloš Kosterec |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Discrete mathematics
Cantor's theorem Theoretical computer science 010102 general mathematics General Social Sciences Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) 06 humanities and the arts Type (model theory) 0603 philosophy ethics and religion Mathematical proof 01 natural sciences Cardinality of the continuum Set (abstract data type) Philosophy symbols.namesake Cardinality Schröder–Bernstein theorem 060302 philosophy symbols 0101 mathematics Type constructor Mathematics |
| Zdroj: | Synthese. 194:5005-5021 |
| ISSN: | 1573-0964 0039-7857 |
| DOI: | 10.1007/s11229-016-1190-1 |
| Popis: | In this paper, I investigate type theories (TTs) from several perspectives. First, I present and elaborate the philosophical and technical motivations for these theories. I then offer a formal analysis of various TTs, focusing on the cardinality of the set of types contained in each. I argue that these TTs can be divided into four formal categories, which are derived from the cardinality of the set of their basic elementary types and the finiteness of the lengths of their molecular types. The paper provides proofs of the cardinality of the universe of types for each of the specified theories. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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