On the definability of the quantifier “there exist uncountably many”

✍ Scribed by Žarko Mijajlović

• Book ID: 104754316
• Publisher: Springer Netherlands
• Year: 1985
• Tongue: English
• Weight: 401 KB
• Volume: 44
• Category: Article
• ISSN: 0039-3215
• DOI: 10.1007/bf00394445

✦ Synopsis

In paper [5] i~ was shown that a great par~ of model theory of logic with the generalized quantifier Qx = "there exist uneountably many x" is reducible to the model theory of firs~ order 16gie with an extra binary r~la~ion symbol. In this paper we consider when the quantifier Qm can be "syntactically" defined in ~ firs~ order theory T. That problem was raised by Kosta Do~en when he asked if r quan-tKier Qx can be eliminated in Peano arithmetic. We answer that (tuestion fully in this paper.