König's Infinity Lemma and Beth's Tree Theorem
| Autor: | George Weaver |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Discrete mathematics
History Lemma (mathematics) Graph theoretic 010102 general mathematics 06 humanities and the arts 0603 philosophy ethics and religion 01 natural sciences Logical consequence Graph Combinatorics History and Philosophy of Science 060302 philosophy König's lemma Teichmüller–Tukey lemma 0101 mathematics Mathematics |
| Zdroj: | History and Philosophy of Logic. 38:48-56 |
| ISSN: | 1464-5149 0144-5340 |
| DOI: | 10.1080/01445340.2015.1065460 |
| Popis: | Konig, D. [1926. ‘Sur les correspondances multivoques des ensembles’, Fundamenta Mathematica, 8, 114–34] includes a result subsequently called Konig's Infinity Lemma. Konig, D. [1927. ‘Uber eine Schlussweise aus dem Endlichen ins Unendliche’, Acta Litterarum ac Scientiarum, Szeged, 3, 121–30] includes a graph theoretic formulation: an infinite, locally finite and connected (undirected) graph includes an infinite path. Contemporary applications of the infinity lemma in logic frequently refer to a consequence of the infinity lemma: an infinite, locally finite (undirected) tree with a root has a infinite branch. This tree lemma can be traced to [Beth, E. W. 1955. ‘Semantic entailment and formal derivability’, Mededelingen der Kon. Ned. Akad. v. Wet., new series 18, 13, 309–42]. It is argued that Beth independently discovered the tree lemma in the early 1950s and that it was later recognized among logicians that Beth's result was a consequence of the infinity lemma. The equivalence of these lemmas is an easy ... |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|