First order irrationality criteria for series

Research output: Contribution to journalArticle (Academic Journal)peer-review


Following a question of Brun, we consider the possibility of finding a first order statement that the rational summands in an infinite series can be checked against in order to give a sufficient condition for the series to sum to an irrational value. We show that such a statement can exist in structures that define the integers, but not in o-minimal structures.
Original languageEnglish
Pages (from-to)1-15
Number of pages15
JournalJournal of Logic and Analysis
Issue number1
Publication statusPublished - Feb 2015


  • irrationality criteria


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