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Tree indiscernibilities, revisited

Byunghan Kim, Hyeung-Joon Kim, Lynn Scow
2013 Archive for Mathematical Logic  
We give definitions that distinguish between two notions of indiscernibility for a set {a_η|η∈} that saw original use in sh90, which we name - and -indiscernibility.  ...  The third author was supported by the NSF-AWM Mentoring Travel Grant. tree-indexed indiscernible. Tree-indexed indiscernibles have been studied in several places, among them [3, 2] .  ...  One property that cannot in general be modeled by ss-indiscernibles is the tree property.  ... 
doi:10.1007/s00153-013-0363-6 fatcat:6pqnwaobkff5lkykikwwjns6jq

Page 4447 of Mathematical Reviews Vol. , Issue 99g [page]

1999 Mathematical Reviews  
Axioms of fuzzy implication revisited. (English summary) Fuzzy Sets and Systems 100 (1998), no. 1-3, 267-272.  ...  identity (given a par- tition C ona set U of objects, u and v in U are indiscernible iff they belong to the same block of C; indiscernibility of elements is then extended to indiscernibility of valuations  ... 

Page 1689 of Mathematical Reviews Vol. 55, Issue 6 [page]

1978 Mathematical Reviews  
The proof of this theorem uses indiscernibles.  ...  A Morley tree of height p is a complete binary branching tree of height » in which (i) at each node there is a formula in one free variable vy (with parameters in a single model of 7), (ii) the formulae  ... 

Page 4879 of Mathematical Reviews Vol. , Issue 2004f [page]

2004 Mathematical Reviews  
Summary: “We revisit the issue of epistemological and seman- tic foundations for autoepistemic and default logics, two leading formalisms in nonmonotonic reasoning.  ...  4879 68T Artificial intelligence homogeneous partitions as decision trees or algebraic decision diagrams.” 2004f:68144 68T20 68T40 68w40 Koenig, Sven (1-GAIT-CC; Atlanta, GA); Tovey, Craig (1-GAIT-CC;  ... 

Page 6499 of Mathematical Reviews Vol. , Issue 98J [page]

1998 Mathematical Reviews  
We find a simple account of it by means of a single operation on finite ordered trees. To deal with the cut operator one more operation is needed.  ...  John (4-EDIN-FC; Edinburgh); Takeyama, Makoto (S-CHGT-C; Géteborg) ; Tennent, Robert D. (3-QEN-C; Kingston, ON) Syntactic control of interference revisited.  ... 

Characterization of NIP theories by ordered graph-indiscernibles

Lynn Scow
2012 Annals of Pure and Applied Logic  
We show that a theory T is NIP if and only if every quantifier-free-weakly-saturated ρ g -indiscernible in a model of T is an indiscernible sequence.  ...  We generalize the Unstable Formula Theorem characterization of stable theories in [13] : that a theory T is stable just in case any infinite indiscernible sequence in a model of T is an indiscernible set  ...  Neither of these outcomes is a 2-full binary tree indiscernible witnessing SOP 2 .  ... 
doi:10.1016/j.apal.2011.12.013 fatcat:4lf4bwelvnc7tcf6cysq3nhce4

Set theory with a proper class of indiscernibles [article]

Ali Enayat
2022 arXiv   pre-print
We investigate an extension of ZFC set theory (in an extended language) that stipulates the existence of a proper class of indiscernibles over the universe.  ...  The following theorem is well-known; the equivalence of (a) and (b) will be revisited in Remark 4.3.  ...  In particular, τ F is a well-founded tree.  ... 
arXiv:2008.07706v4 fatcat:e4i7kjpcyvamdcxm3l6g7w3nxa

Set theory with a proper class of indiscernibles

Ali Enayat
2022 Fundamenta Mathematicae  
We investigate an extension of ZFC set theory, denoted ZFI<, which is equipped with a well-ordering < of the universe V of set theory, and a proper class I of indiscernibles over (V, ∈, <).  ...  focus of this paper is on an extension ZFI < of Zermelo-Fraenkel set theory ZF that is equipped with a global wellordering < and a proper class I of ordinals such that (I, ∈) is a collection of order indiscernibles  ...  The following theorem is well-known; the equivalence of (a) and (b) will be revisited in Remark 4.3.  ... 
doi:10.4064/fm999-2-2022 fatcat:4cqlmjybvrhrngwfqqir6ahpeq

Page 3185 of Mathematical Reviews Vol. , Issue 2003e [page]

2003 Mathematical Reviews  
Quantifier elimination is proved for differentially closed fields (these are frequently revisited in the book).  ...  The local tree-width of a structure & isa function f:N—N that for each r computes the maximum tree-width of an r-neighborhood in /.  ... 

Persistence and NIP in the characteristic sequence [article]

M. E. Malliaris
2009 arXiv   pre-print
Specifically, we show that some tree properties are detected by the presence of certain combinatorial configurations in the characteristic sequence while other properties such as instability and the independence  ...  ((ω, n)-arrays revisited) Assume n ≤ r < ω.  ...  Call any such X a ϕ-tree, or if necessary a ϕ-k-tree. • the tree property if it has the k-tree property for some 2 ≤ k < ω. • the non-strict tree property T P 2 if there exists a ϕ-tree with k = 2 and  ... 
arXiv:0908.4111v1 fatcat:skxyylvml5gxtfiqq4ursnec4a

The characteristic sequence of a first-order formula

M. E. Malliaris
2010 Journal of Symbolic Logic (JSL)  
Specifically, we show that some tree properties are detected by the presence of certain combinatorial configurations in the characteristic sequence while other properties such as instability and the independence  ...  ((ω, n)-arrays revisited) Assume n ≤ r < ω.  ...  Call any such X a ϕ-tree, or if necessary a ϕ-k-tree. • the tree property if it has the k-tree property for some 2 ≤ k < ω. • the strict tree property, also known as T P 1 or SOP 2 , if there exists a  ... 
doi:10.2178/jsl/1286198155 fatcat:g5urf7jdy5awdat67hagq252ly

Page 3849 of Mathematical Reviews Vol. , Issue 98F [page]

1998 Mathematical Reviews  
-9); Adrian Atanasiu and Radu Gram- atovici, Learning from examples (10-23); Tudor Balanescu and Marian Gheorghe, Contextual cooperating grammar systems (24- 29); Barron Brainerd, Marcus’ drama model revisited  ...  Mihalache, On parallel communicating grammar systems with context-free components (258-270); Victor Mitrana, Contextual insertion and deletion (271-278); Zdzislaw Pawlak, On some issues connected with indiscernibility  ... 

Bootstrapping, part I

S. Boughattas, J.-P. Ressayre
2010 Annals of Pure and Applied Logic  
Erdos-Rado defined a tree relation on K called the Erdos-Rado tree which is such that all branches of the tree are preindiscernible w.r.t.  ...  We call "tree of height m" the tree T m (ordered by inclusion) of all possible 1-types over < m elements that start with 0, 1, . . ., h − 1.  ... 
doi:10.1016/j.apal.2009.03.004 fatcat:h5rxjsjtjzazjj5meuugfxv7sy

Page 3064 of Mathematical Reviews Vol. , Issue 94f [page]

1994 Mathematical Reviews  
Smith, An interpetation of Kleene’s slash in type theory (189-197); Healfdene Goguen and Zhaohui Luo, Inductive data types: well-ordering types revisited (198-218); Franco Barbanera and Stefano Berardi  ...  19); Kojiro Kobayashi, On malign input distributions for algo- rithms (20-34); Libo Lo [Li Bo Luo], Research on the theory of finite models without equalities (35-41); Tadatoshi Miyamoto, @)- Souslin trees  ... 

Page 561 of Mathematical Reviews Vol. , Issue 2003A [page]

2003 Mathematical Reviews  
Andrés Cano and Serafin Moral, Computing intervals of prob- abilities with simulated annealing and probability trees (278- 289); Veronica Biazzo, Angelo Gilio, Thomas Lukasiewicz and Giuseppe Sanfilippo  ...  construction of R from Z (43-58); Andrea Asperti, Luca Padovani, Claudio Sacerdoti Coen and Irene Schena, HELM and the semantic math-web (59-74); Gertrud Bauer and Markus Wen- zel, Calculational reasoning revisited  ... 
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