An ultrapower which does not preserve the truth of a \(\Pi_2\) sentence (Q1961890)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: An ultrapower which does not preserve the truth of a \(\Pi_2\) sentence |
scientific article; zbMATH DE number 1394748
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An ultrapower which does not preserve the truth of a \(\Pi_2\) sentence |
scientific article; zbMATH DE number 1394748 |
Statements
An ultrapower which does not preserve the truth of a \(\Pi_2\) sentence (English)
0 references
23 March 2000
0 references
Working in the ordered Mostowski permutation model, the author shows that in the absence of the axiom of choice the property ``ordered subset without endpoints'' need not be preserved by ultraproducts. This result exemplifies Howard's theorem that Los' theorem together with the Boolean prime ideal theorem are equivalent to the axiom of choice.
0 references
ordered Mostowski permutation model
0 references
axiom of choice
0 references
ultraproducts
0 references
Los' theorem
0 references
Boolean prime ideal theorem
0 references
0.8212857
0 references
0.8140039
0 references
0.80732113
0 references
0.7969881
0 references
0 references
0.7832455
0 references
