Existence of some sparse sets of nonstandard natural numbers

Journal of Symbolic Logic 66 (2):959-973 (2001)
Answers are given to two questions concerning the existence of some sparse subsets of $\mathscr{H} = \{0, 1,..., H - 1\} \subseteq * \mathbb{N}$ , where H is a hyperfinite integer. In § 1, we answer a question of Kanovei by showing that for a given cut U in H, there exists a countably determined set $X \subseteq \mathscr{H}$ which contains exactly one element in each U-monad, if and only if U = a · N for some $a \in \mathscr{H} \backslash \{0\}$ . In §2, we deal with a question of Keisler and Leth in [6]. We show that there is a cut $V \subseteq \mathscr{H}$ such that for any cut U, (i) there exists a U-discrete set $X \subseteq \mathscr{H}$ with X + X = H (mod H) provided $U \subsetneqq V$ , (ii) there does not exist any U-discrete set $X \subseteq \mathscr{H}$ with X + X = H (mod H) provided $\supsetneqq V$ . We obtain some partial results for the case U = V
Keywords Hyperfinite Integer   Cut   Countably Determined Set   U-Discrete Set
Categories (categorize this paper)
DOI 10.2307/2695055
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
Download options
PhilPapers Archive

Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 23,674
External links
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Monthly downloads

Added to index


Total downloads

14 ( #312,074 of 1,903,046 )

Recent downloads (6 months)

1 ( #446,009 of 1,903,046 )

How can I increase my downloads?

My notes
Sign in to use this feature

Start a new thread
There  are no threads in this forum
Nothing in this forum yet.