A Reflection Principle As a Reverse-mathematical Fixed Point over the Base Theory ZFC

AbstractWe prove that the theory of the extensional compositional truth predicate for the language of arithmetic with Δ0-induction scheme for the truth predicate and the full arithmetical induction scheme is not conservative over Peano Arithmetic. In addition, we show that a slightly modified theory of truth actually proves the global reflection principle over the base theory.

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Computable aspects of the Bachmann–Howard principle

Journal of Mathematical Logic ◽

10.1142/s0219061320500063 ◽

2019 ◽

Vol 20 (02) ◽

pp. 2050006 ◽

Cited By ~ 2

Author(s):

Anton Freund

Keyword(s):

Fixed Point ◽

Text Comprehension ◽

Transformation Formula ◽

Notation System ◽

Base Theory ◽

Well Foundedness

We have previously established that [Formula: see text]-comprehension is equivalent to the statement that every dilator has a well-founded Bachmann–Howard fixed point, over [Formula: see text]. In this paper, we show that the base theory can be lowered to [Formula: see text]. We also show that the minimal Bachmann–Howard fixed point of a dilator [Formula: see text] can be represented by a notation system [Formula: see text], which is computable relative to [Formula: see text]. The statement that [Formula: see text] is well founded for any dilator [Formula: see text] will still be equivalent to [Formula: see text]-comprehension. Thus, the latter is split into the computable transformation [Formula: see text] and a statement about the preservation of well-foundedness, over a system of computable mathematics.

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Mental equilibrium: Identifying fixed-point attractors in the stream of thought

PsycEXTRA Dataset ◽

10.1037/e633872013-031 ◽

2003 ◽

Author(s):

Robin R. Vallacher ◽

Andrzej Nowak ◽

Matthew Rockloff

Keyword(s):

Fixed Point

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ON THE RANDOM FIXED POINT THEOREMS IN ABSTRACT SPACE

Acta Mathematica Scientia ◽

10.1016/s0252-9602(18)30707-0 ◽

1981 ◽

Vol 1 (2) ◽

pp. 133-144 ◽

Cited By ~ 2

Author(s):

Shaozhong Chen ◽

Zuoshu Liu

Keyword(s):

Fixed Point ◽

Fixed Point Theorems ◽

Abstract Space ◽

Random Fixed Point

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Fixed point model for adaptive token passing bus protocol

IEE Proceedings E Computers and Digital Techniques ◽

10.1049/ip-e.1992.0007 ◽

1992 ◽

Vol 139 (1) ◽

pp. 50 ◽

Cited By ~ 2

Author(s):

P.G. Harrison ◽

F. Naraghi

Keyword(s):

Fixed Point ◽

Point Model ◽

Token Passing

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Bifurcation in a Simple Model of the Cardiovascular System

Methods of Information in Medicine ◽

10.1055/s-0038-1634285 ◽

2000 ◽

Vol 39 (02) ◽

pp. 118-121 ◽

Cited By ~ 5

Author(s):

S. Akselrod ◽

S. Eyal

Keyword(s):

Nonlinear Dynamics ◽

Blood Pressure ◽

Heart Rate ◽

Fixed Point ◽

Cardiovascular System ◽

Modified Model ◽

Mayer Waves ◽

Sustained Oscillations ◽

Human Cardiovascular System ◽

Physiological Values

Abstract:A simple nonlinear beat-to-beat model of the human cardiovascular system has been studied. The model, introduced by DeBoer et al. was a simplified linearized version. We present a modified model which allows to investigate the nonlinear dynamics of the cardiovascular system. We found that an increase in the -sympathetic gain, via a Hopf bifurcation, leads to sustained oscillations both in heart rate and blood pressure variables at about 0.1 Hz (Mayer waves). Similar oscillations were observed when increasing the -sympathetic gain or decreasing the vagal gain. Further changes of the gains, even beyond reasonable physiological values, did not reveal another bifurcation. The dynamics observed were thus either fixed point or limit cycle. Introducing respiration into the model showed entrainment between the respiration frequency and the Mayer waves.

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