Peano arithmetic may not be interpretable in the monadic theory of linear orders

1997 ◽  
Vol 62 (3) ◽  
pp. 848-872 ◽  
Author(s):  
Shmuel Lifsches ◽  
Saharon Shelah
Keyword(s):  
Real Line ◽  
Order Theory ◽  
Peano Arithmetic ◽  
Second Order ◽  
Linear Orders ◽  
The Real ◽  
Monadic Theory

AbstractGurevich and Shelah have shown that Peano Arithmetic cannot be interpreted in the monadic second-order theory of short chains (hence, in the monadic second-order theory of the real line). We will show here that it is consistent that the monadic second-order theory of no chain interprets Peano Arithmetic.

On the strength of the interpretation method

1989 ◽  
Vol 54 (2) ◽  
pp. 305-323 ◽  
Author(s):  
Yuri Gurevich ◽  
Saharon Shelah
Keyword(s):  
Real Line ◽  
Order Theory ◽  
Peano Arithmetic ◽  
Second Order ◽  
The Real ◽  
Interpretation Method

AbstractIn spite of the fact that true arithmetic reduces to the monadic second-order theory of the real line, Peano arithmetic cannot be interpreted in the monadic second-order theory of the real line.

Dependent thinning of point processes

1980 ◽  
Vol 17 (04) ◽  
pp. 987-995 ◽  
Author(s):  
Valerie Isham
Keyword(s):  
Poisson Process ◽  
Point Process ◽  
Real Line ◽  
Point Processes ◽  
Compound Poisson Process ◽  
Second Order ◽  
Binary Variables ◽  
Compound Poisson ◽  
The Real ◽  
Markov Sequence

A point process, N, on the real line, is thinned using a k -dependent Markov sequence of binary variables, and is rescaled. Second-order properties of the thinned process are described when k = 1. For general k, convergence to a compound Poisson process is demonstrated.

Do children understand that people selectively conceal or express emotion?

2014 ◽  
Vol 39 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Hajimu Hayashi ◽  
Yuki Shiomi
Keyword(s):  
First Graders ◽  
Negative Emotion ◽  
Fifth Graders ◽  
Order Theory ◽  
Third Graders ◽  
Second Order ◽  
The Other ◽  
The Real ◽  
Express Emotion ◽  
Negative Feelings

This study examined whether children understand that people selectively conceal or express emotion depending upon the context. We prepared two contexts for a verbal display task for 70 first-graders, 80 third-graders, 64 fifth-graders, and 71 adults. In both contexts, protagonists had negative feelings because of the behavior of the other character. In the prosocial context, children were instructed that the protagonist wished to spare the other character’s feelings. In contrast, in the real-emotion context, children were told that the protagonist was fed up with the other character’s behavior. Participants were asked to imagine what the protagonists would say. Adults selected utterances with positive or neutral emotion in the prosocial context but chose utterances with negative emotion in the real-emotion context, whereas first-graders selected utterances with negative emotion in both contexts. In the prosocial context, the proportion of utterances with negative emotion decreased from first-graders to adults, whereas in the real-emotion context the proportion was U-shaped, decreasing from first- to third-graders and increasing from fifth-graders to adults. Further, performance on both contexts was associated with second-order false beliefs as well as second-order intention understanding. These results indicate that children begin to understand that people selectively conceal or express emotion depending upon context after 8 to 9 years. This ability is also related to second-order theory of mind.

The monadic theory of ω2

1983 ◽  
Vol 48 (2) ◽  
pp. 387-398 ◽  
Author(s):  
Yuri Gurevich ◽  
Menachem Magidor ◽  
Saharon Shelah
Keyword(s):  
Order Theory ◽  
Second Order ◽  
The Other ◽  
Weakly Compact ◽  
Compact Cardinal ◽  
Monadic Theory ◽  
Weakly Compact Cardinal

AbstractAssume ZFC + “There is a weakly compact cardinal” is consistent. Then:(i) For every S ⊆ ω, ZFC + “S and the monadic theory of ω2 are recursive each in the other” is consistent; and(ii) ZFC + “The full second-order theory of ω2 is interpretable in the monadic theory of ω2” is consistent.

Dependent thinning of point processes

1980 ◽  
Vol 17 (4) ◽  
pp. 987-995 ◽  
Author(s):  
Valerie Isham
Keyword(s):  
Poisson Process ◽  
Point Process ◽  
Real Line ◽  
Point Processes ◽  
Compound Poisson Process ◽  
Second Order ◽  
Binary Variables ◽  
Compound Poisson ◽  
The Real ◽  
Markov Sequence

A point process, N, on the real line, is thinned using a k -dependent Markov sequence of binary variables, and is rescaled. Second-order properties of the thinned process are described when k = 1. For general k, convergence to a compound Poisson process is demonstrated.

scholarly journals The empirical mean position of a branching Lévy process

2020 ◽  
Vol 57 (4) ◽  
pp. 1252-1259
Author(s):  
David Cheek ◽  
Seva Shneer
Keyword(s):  
Limit Theorem ◽  
Real Line ◽  
Lévy Process ◽  
Second Order ◽  
Levy Process ◽  
The Real

AbstractWe consider a supercritical branching Lévy process on the real line. Under mild moment assumptions on the number of offspring and their displacements, we prove a second-order limit theorem on the empirical mean position.

Sign in / Sign up

Export Citation Format

Share Document