کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4662912 | 1633616 | 2016 | 12 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Representable posets
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
منطق ریاضی
چکیده انگلیسی
A poset is representable if it can be embedded in a field of sets in such a way that existing finite meets and joins become intersections and unions respectively (we say finite meets and joins are preserved). More generally, for cardinals α and β a poset is said to be (α,β)-representable if an embedding into a field of sets exists that preserves meets of sets smaller than α and joins of sets smaller than β. We show using an ultraproduct/ultraroot argument that when 2â¤Î±,βâ¤Ï the class of (α,β)-representable posets is elementary, but does not have a finite axiomatization in the case where either α or β=Ï. We also show that the classes of posets with representations preserving either countable or all meets and joins are pseudoelementary.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Applied Logic - Volume 16, July 2016, Pages 60-71
Journal: Journal of Applied Logic - Volume 16, July 2016, Pages 60-71
نویسندگان
Rob Egrot,