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A new method for undecidability proofs of first order theories

1992
*
Journal of symbolic computation
*

*First*it proposes

*a*general methodology

*for*proving results

*of*the kind : The

*first*

*order*

*theory*

*of*the predicate logic model I = . . . is

*undecidable*. ... We claim that the reduction

*of*Post's Correspondence Problem to the decision problem

*of*

*a*

*theory*provides

*a*useful tool

*for*proving

*undecidability*

*of*

*first*

*order*

*theories*given by some interpretation. ...

*A*

*New*

*Method*

*for*

*Undecidability*

*Proofs*

*of*

*First*

*Order*

*Theories*RALF TREINEN DFKI, Stuhlsatzenhausweg S, W6600 Saarbrucken Germany (Received 21 March 1991) We claim that the reduction

*of*Post's Correspondence ...

##
###
A new method for undecidability proofs of first order theories
[chapter]

1990
*
Lecture Notes in Computer Science
*

*First*it proposes

*a*general methodology

*for*proving results

*of*the kind : The

*first*

*order*

*theory*

*of*the predicate logic model I = . . . is

*undecidable*. ... We claim that the reduction

*of*Post's Correspondence Problem to the decision problem

*of*

*a*

*theory*provides

*a*useful tool

*for*proving

*undecidability*

*of*

*first*

*order*

*theories*given by some interpretation. ...

*A*

*New*

*Method*

*for*

*Undecidability*

*Proofs*

*of*

*First*

*Order*

*Theories*RALF TREINEN DFKI, Stuhlsatzenhausweg S, W6600 Saarbrucken Germany (Received 21 March 1991) We claim that the reduction

*of*Post's Correspondence ...

##
###
Page 6087 of Mathematical Reviews Vol. , Issue 87k
[page]

1987
*
Mathematical Reviews
*

The

*method**of**proof*is as follows.*First*an observation*of*Jensen is applied to deduce*a*weak form*of*the square principle from the existence*of**a**A**-special Aronszajn tree. ...*A*previous paper*of*the author {same journal 32 (1986), no. 1, 29-44; MR 87i:03108] gave*a**new**first*-*order*axiomatization*of*H. M. ...##
###
Undecidability of free pseudocomplemented semilattices

1987
*
Publications of the Research Institute for Mathematical Sciences
*

Decision problem

doi:10.2977/prims/1195176449
fatcat:j7zjypqjffg4lm4pqdjl7qhwcy
*for*the*first**order**theory**of*free objects in equational classes*of*algebras was investigated*for*groups (Malcev [10]), semigroups (Quine [12]), commutative semigroups (Mostowski [11]) ...*For*Sen let 33 5 denote the pcs obtained from the lattice 2 s*of*all subsets*of*S by adjoining*a**new*smallest element 0 5 . ... He would like to thank Professor Hiroakira Ono*for*his hospitality, ...##
###
Undecidability, unit groups, and some totally imaginary infinite extensions of Q
[article]

2020
*
arXiv
*
pre-print

We produce

arXiv:1910.01239v2
fatcat:v4sg5twlendnll3keyww2a2eti
*new*examples*of*totally imaginary infinite extensions*of*Q which have*undecidable**first*-*order**theory*by generalizing the*methods*used by Martinez-Ranero, Utreras and Videla*for*Q^(2). ... This proves the*undecidability**of*Q^(d)_ab*for*all d ≥ 2. ... Clearly, if O L is definable in L and the*first*-*order**theory**of*O L is*undecidable*, then the*first*-*order**theory**of*L is also*undecidable*. ...##
###
Eleventh Meeting of the Association for Symbolic Logic

1949
*
Journal of Symbolic Logic (JSL)
*

*A*

*new*mathematical

*proof*

*for*

*a*variant

*of*transfinite induction up to the

*first*epsilonnumber is given. The

*proof*is (i) capable

*of*generalization, (ii)

*of*metamathematical interest. 16. C D . ... calculi

*of*

*first*

*order*. ...

##
###
Page 8474 of Mathematical Reviews Vol. , Issue 2004k
[page]

2004
*
Mathematical Reviews
*

The same holds

*for*the*first*-*order*logic*of**proofs*with monotonicity axiom QLP®. ... The*proof**of*the upper bound shows the standard*methods**of*infinitary*proof**theory*at work. ...##
###
On 2nd order intuitionistic propositional calculus with full comprehension

1974
*
Archive for Mathematical Logic
*

The

doi:10.1007/bf02015377
fatcat:pndaucaiv5bjfkjubqj3l2bj2i
*proof**of**undecidability*uses the same*method*introduced in Gabbay [3, 4] and used to obtain*undecidability*results*for**a*large class*of*intuitionistic*theories*. ... Kit Fine has obtained*undecidability*results*for*2nd*order*modal logics. ...##
###
Decidable and undecidable logics with a binary modality

1995
*
Journal of Logic, Language and Information
*

is on those parts

doi:10.1007/bf01049412
fatcat:ggzx4o3opbhqni6wbnhhpceeaa
*of*the*proof**methods*which have been well known*for*the specialists. ... We put an emphasis on the demonstration*of**proof*-techniques, and hope that this will also help in finding the borderlines between decidable and*undecidable*fragments*of*usual*first*-*order*logic. ... We are especially grateful to Steven Givant*for*extensive help. ...##
###
Alfred Tarski and undecidable theories

1986
*
Journal of Symbolic Logic (JSL)
*

We will say that

doi:10.2307/2273902
fatcat:iav44bpgjrgztkhoxpotrfruge
*a*set*of*elementary sentences is*a**theory*provided it is closed with respect to logical consequence and we will say that*a**theory*is decidable or*undecidable*depending on whether it is ... Tarski's work on decidability falls into four broad areas: elementary*theories*which are decidable, elementary*theories*which are*undecidable*, the*undecidability**of**theories**of*various restricted kinds ... Perhaps Tarski's most far-reaching contribution to our understanding*of**undecidable**theories*is the paper*A*general*method*in*proofs**of**undecidability*, which is the*first**of*the three papers that comprise ...##
###
New formally undecidable propositions: non-trivial lower bounds on proof complexity and related theorems

1991
*
Theoretical Computer Science
*

Thus we have

doi:10.1016/0304-3975(91)90272-4
fatcat:sxrrh4cxefhknccipacsn4r3nu
*a**new*large class*of*formally*undecidable*mathematical propositions. ... This is*new*evidence*for*the validity*of*Cook's conjecture. ... I VY,, %I + G*for**first**order*G. We can take F* to be*a*sequence*of*such*first**order*approximations to F. ...##
###
Page 750 of Mathematical Reviews Vol. 55, Issue 3
[page]

1978
*
Mathematical Reviews
*

Logik Grundlagen Math. 14 (1968), 457-472; MR 38 #5620] showed that the

*first**order**theory**of*2 is*undecidable*, and his*proof*shows that the degree*of*this*theory*is at least 0’. ... The author gives*a**new**method**of*constructing initial segments*of*degrees*of**order*type w based on the idea*of*iterated forcing. ...##
###
A Proof of Syntactic Incompleteness of the Second-Order Categorical Arithmetic

2017
*
OALib
*

Nor is it legitimate to assert that the

doi:10.4236/oalib.1103969
fatcat:fbsqz43skvgjhn3nvpi2rlzcwi
*undecidability**of*the statements is generally kept in passing from*a*certain*theory*(such as PA) to another that includes it (such as AR). ... Pending*a*response to the previous question, this paper aims to present*a**proof**of*the syntactic/semantical incompleteness*of*AR, by examples based on the different modes*of*representation (i.e. codes) ... Here the Gödel's famous statement (G),*undecidable*in PA, still means "no gödelian code*of**a**proof**of*myself exists" but no longer "I'm not*a*theorem", since not every*proof*has*a*gödelian code (those ...##
###
Page 6434 of Mathematical Reviews Vol. , Issue 96k
[page]

1996
*
Mathematical Reviews
*

As an application, he proves hereditary

*undecidability**for*£,-*theories**of*some natural classes*of*finite structures, such as graphs, lattices, and partial*orders*, as well as natural structures arising ... The*new*metatheorem grew, in part, out*of*an effort to find*a**new**proof**of*Ash’s metatheorem. The*new*metatheorem yields the one in [C. J. Ash, op. cit; MR 91g:03090], and it seems more flexible. ...##
###
Definability and decidability for rings of integers in totally imaginary fields
[article]

2022
*
arXiv
*
pre-print

This implies that the ring

arXiv:2207.00140v1
fatcat:eu5bxn32end7pnyshma66pgueu
*of*integers*of*ℚ^tr(i) is*undecidable*and*first*-*order*non-definable in ℚ^tr(i). ... More generally, when L is*a*totally imaginary quadratic extension*of**a*totally real field K, we use the unit groups R^×*of**orders*R⊆𝒪_L to produce existentially definable totally real subsets X⊆𝒪_L. ... Namely, in the context*of*Theorem 3.4, if the existential or*first**order**theory**of*OK is*undecidable*then the same is true*for*OL . ...
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