Finite Language Forbidding-Enforcing Systems

Author(s):  
Daniela Genova ◽  
Hendrik Jan Hoogeboom
Keyword(s):  
2000 ◽  
Vol 10 (04) ◽  
pp. 457-480 ◽  
Author(s):  
OLGA SAPIR

Let W be a finite language and let Wc be the closure of W under taking subwords. Let S(W) denote the Rees quotient of a free monoid over the ideal consisting of all words that are not in Wc. We call W finitely based if the monoid S(W) is finitely based. Although these semigroups have easy structure they behave "generically" with respect to the finite basis property [6]. In this paper, we describe all finitely based words in a two-letter alphabet. We also find some necessary and some sufficient conditions for a set of words to be finitely based.


1990 ◽  
Vol 55 (2) ◽  
pp. 626-636
Author(s):  
John T. Baldwin

AbstractLet T be a complete countable first order theory and λ an uncountable cardinal. Theorem 1. If T is not superstable, T has 2λ resplendent models of power λ. Theorem 2. If T is strictly superstable, then T has at least min(2λ, ℶ2) resplendent models of power λ. Theorem 3. If T is not superstable or is small and strictly superstable, then every resplendent homogeneous model of T is saturated. Theorem 4 (with Knight). For each μ ∈ ω ∪ {ω, 2ω} there is a recursive theory in a finite language which has μ resplendent models of power κ for every infinite κ.


2001 ◽  
Vol 66 (4) ◽  
pp. 1766-1782 ◽  
Author(s):  
Ali Enayat

Abstract.A model = (M. E, …) of Zermelo-Fraenkel set theory ZF is said to be 0-like. where E interprets ∈ and θ is an uncountable cardinal, if ∣M∣ = θ but ∣{b ∈ M: bEa}∣ < 0 for each a ∈ M, An immediate corollary of the classical theorem of Keisler and Morley on elementary end extensions of models of set theory is that every consistent extension of ZF has an ℵ1-like model. Coupled with Chang's two cardinal theorem this implies that if θ is a regular cardinal 0 such that 2<0 = 0 then every consistent extension of ZF also has a 0+-like model. In particular, in the presence of the continuum hypothesis every consistent extension of ZF has an ℵ2-like model. Here we prove:Theorem A. If 0 has the tree property then the following are equivalent for any completion T of ZFC:(i) T has a 0-like model.(ii) Ф ⊆ T. where Ф is the recursive set of axioms {∃κ (κ is n-Mahlo and “Vκis a Σn-elementary submodel of the universe”): n ∈ ω}.(iii) T has a λ-like model for every uncountable cardinal λ.Theorem B. The following are equiconsistent over ZFC:(i) “There exists an ω-Mahlo cardinal”.(ii) “For every finite language , all ℵ2-like models of ZFC() satisfy the schemeФ().


2000 ◽  
Vol 65 (1) ◽  
pp. 187-200 ◽  
Author(s):  
Ross Willard

AbstractWe derive a Mal'cev condition for congruence meet-semidistributivity and then use it to prove two theorems. Theorem A: if a variety in a finite language is congruence meet-semidistributive and residually less than some finite cardinal, then it is finitely based. Theorem B: there is an algorithm which, given m < ω and a finite algebra in a finite language, determines whether the variety generated by the algebra is congruence meet-semidistributive and residually less than m.


2011 ◽  
Vol 76 (3) ◽  
pp. 883-896 ◽  
Author(s):  
Uri Andrews

AbstractWe employ an infinite-signature Hrushovski amalgamation construction to yield two results in Recursive Model Theory. The first result, that there exists a strongly minimal theory whose only recursively presentable models are the prime and saturated models, adds a new spectrum to the list of known possible spectra. The second result, that there exists a strongly minimal theory in a finite language whose only recursively presentable model is saturated, gives the second non-trivial example of a spectrum produced in a finite language.


2014 ◽  
Vol 18 (3) ◽  
pp. 349-372 ◽  
Author(s):  
Eric Stenclik

When American poet Hart Crane declares in a letter, “I felt the two worlds. And at once,” he speaks bluntly of the governing tension of his poetry: the knocking of Harold Hart Crane’s finite language against the hard, transparent ceiling beyond which he senses the divine. Crane’s first collection, White Buildings, often shows signs of visionary frustration. But in “Lachrymae Christi,” the most difficult poem in White Buildings, Crane’s vision dilates to immense possibilities of union between the material and the spirit worlds, between what is time-bound and what is timeless. This poem, both its poetic effect and its spiritual purpose, can be most sympathetically read as mystical. Because the tonal movement toward rapture in “Lachrymae Christi” resonates against the poetry and theology of Renaissance mystics such as St. John of the Cross, we can situate the poem in the context of ancient patterns of western mysticism in order to reclaim what has long been seen as an opaque and elusive poem. “Lachrymae Christi” rewards this reading of its mystical poetics with line after line of quivering wordplay, startlingly fresh religious allusion, and subtle thematic polyphony as it interweaves Christian and pagan traditions of regeneration.


Integers ◽  
2011 ◽  
Vol 11 (6) ◽  
Author(s):  
Stefan Gerhold

AbstractWe investigate the number of sets of words that can be formed from a finite alphabet, counted by the total length of the words in the set. An explicit expression for the counting sequence is derived from the generating function, and asymptotics for large alphabet size and large total word length are discussed. Moreover, we derive a Gaussian limit law for the number of words in a random finite language.


2008 ◽  
Vol 19 (01) ◽  
pp. 243-250 ◽  
Author(s):  
ANTON ČERNÝ

We call a word L-symmetric with respect to a finite language L if it contains the same number of scattered subwords u as of uR for every word u from L. We show that increasing the size of the language L may lead to an unlimited refinement of the language of L-symmetric words. Further we prove that if a long enough initial segment of a D0L-sequence consists entirely of L-symmetric words, then all words in the sequence are L-symmetric.


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