432 research outputs found
Ehrenfeucht-Fraïssé games without identity
This note defines Ehrenfeucht-Fraïssé games where identity is not present in the basic language. The formulation is applied to show that there is no elementary theory in the language of one binary relation that exactly characterizes models in which the relation is the identity relation
Ehrenfeucht-Fraïssé games without identity
This note defines Ehrenfeucht-Fraïssé games where identity is not present in the basic language. The formulation is applied to show that there is no elementary theory in the language of one binary relation that exactly characterizes models in which the relation is the identity relation
Fixed Points and Attractors of Reactantless and Inhibitorless Reaction Systems
Reaction systems are discrete dynamical systems that model biochemical
processes in living cells using finite sets of reactants, inhibitors, and
products. We investigate the computational complexity of a comprehensive set of
problems related to the existence of fixed points and attractors in two
constrained classes of reaction systems, in which either reactants or
inhibitors are disallowed. These problems have biological relevance and have
been extensively studied in the unconstrained case; however, they remain
unexplored in the context of reactantless or inhibitorless systems.
Interestingly, we demonstrate that although the absence of reactants or
inhibitors simplifies the system's dynamics, it does not always lead to a
reduction in the complexity of the considered problems.Comment: 29 page
On Elementary Theories of Ordinal Notation Systems based on Reflection Principles
We consider the constructive ordinal notation system for the ordinal
that were introduced by L.D. Beklemishev. There are fragments of
this system that are ordinal notation systems for the smaller ordinals
(towers of -exponentiations of the height ). This
systems are based on Japaridze's provability logic . They are
closely related with the technique of ordinal analysis of and
fragments of based on iterated reflection principles. We consider
this notation system and it's fragments as structures with the signatures
selected in a natural way. We prove that the full notation system and it's
fragments, for ordinals , have undecidable elementary theories.
We also prove that the fragments of the full system, for ordinals
, have decidable elementary theories. We obtain some results
about decidability of elementary theory, for the ordinal notation systems with
weaker signatures.Comment: 23 page
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