COUNTING SIBLINGS IN UNIVERSAL THEORIES
نویسندگان
چکیده
We show that if a countable structure $M$ in finite relational language is not cellular, then there an age-preserving $N \supseteq M$ such $2^{\aleph_0}$ many structures are bi-embeddable with $N$. The proof proceeds by case division based on mutual algebraicity.
منابع مشابه
Universal oscillations in counting statistics.
Noise is a result of stochastic processes that originate from quantum or classical sources. Higher-order cumulants of the probability distribution underlying the stochastic events are believed to contain details that characterize the correlations within a given noise source and its interaction with the environment, but they are often difficult to measure. Here we report measurements of the tran...
متن کاملModel Counting Modulo Theories
This thesis is concerned with the quantitative assessment of security in software. More specifically, it tackles the problem of efficient computation of channel capacity, the maximum amount of confidential information leaked by software, measured in Shannon entropy or Rényi’s min-entropy. Most approaches to computing channel capacity are either efficient and return only (possibly very loose) up...
متن کاملUniversal Homotopy Theories
Model categories were introduced by Quillen [Q] to provide a framework through which one could apply homotopy theory in various settings. They have been astonishingly successful in this regard, and in recent years one of the first things one does when studying any homotopical situation is to try to set up a model structure. The aim of this paper is to introduce a new, but very basic, tool into ...
متن کاملFormal Theories for Logspace Counting
We introduce two-sorted theories in the style of Cook and Nguyen for the complexity classes ParityL and DET, whose complete problems include determinants over GF(2) and Z, respectively. The definable functions in these theories are the functions in the corresponding complexity classes; thus each theory formalizes reasoning using concepts from its corresponding complexity class.
متن کاملUniversal Counting of Lattice Points in Polytopes
Given a lattice polytope P (with underlying lattice L), the universal counting function UP (L ) = |P ∩ L| is defined on all lattices L containing L. Motivated by questions concerning lattice polytopes and the Ehrhart polynomial, we study the equation UP = UQ. Mathematics Subject Classification: 52B20, 52A27, 11P21 Partially supported by Hungarian Science Foundation Grant T 016391, and by the Fr...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Symbolic Logic
سال: 2022
ISSN: ['1943-5886', '0022-4812']
DOI: https://doi.org/10.1017/jsl.2022.3