Factorization of the Shoenfield-like bounded functional interpretation

We adapt Streicher and Kohlenbach's proof of the factorization S = KD of the Shoenfield translation S in terms of Krivine's negative translation K and the G\"odel functional interpretation D, obtaining a proof of the factorization U = KB of Ferreira's Shoenfield-like bounded functional interpretation U in terms of K and Ferreira and Oliva's bounded functional interpretation B

On Tao's "finitary" infinite pigeonhole principle

In 2007, Terence Tao wrote on his blog an essay about soft analysis, hard analysis and the finitization of soft analysis statements into hard analysis statements. One of his main examples was a quasi-finitization of the infinite pigeonhole principle IPP, arriving at the "finitary" infinite pigeonhole principle FIPP1. That turned out to not be the proper formulation and so we proposed an alternative version FIPP2. Tao himself formulated yet another version FIPP3 in a revised version of his essay. We give a counterexample to FIPP1 and discuss for both of the versions FIPP2 and FIPP3 the faithfulness of their respective finitization of IPP by studying the equivalences IPP FIPP2 and IPP FIPP3 in the context of reverse mathematics. In the process of doing this we also introduce a continuous uniform boundedness principle CUB as a formalization of Tao's notion of a correspondence principle and study the strength of this principle and various restrictions thereof in terms of reverse mathematics, i.e., in terms of the "big five" subsystems of second order arithmetic

Welfare Policies and Solidarity Toward the Elderly

In this paper we analyze the effect of welfare policies oriented toward the elderly on solidarity toward the elderly in a sample of European countries. The research question is whether more generous welfare policies crowd out solidarity. For this purpose, we analyze four waves of the SHARE database. We use multilevel analysis to estimate the effect of national variables on transfers toward the elderly, controlling for individual level variables. At the national level we focus on the effect of public spending on policies oriented toward the elderly after controlling for some other relevant variables, such as the proportion of elderly people, female labor force participation and unemployment. Our results indicate that expenditure in social protection toward the elderly has a positive and significant (albeit moderate) effect on the economic support received by the elderly (which is in line with the Crowding-in hypothesis). However, in the case of time transfers, we find that expenditure in social protection toward the elderly has a negative and significant impact on the time transfers received by the elderly (which is consistent with the Crowding-out hypothesis).Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Copies of Classical Logic in Intuitionistic Logic

La logique classique (la logique des mathématiques non-constructives) est plus forte que la logique intuitionniste (la logique des mathématiques constructives). Malgré cela, il existe des copies de la logique classique dans la logique intuitionniste. Toutes les copies habituellement trouvées dans la littérature sont les mêmes. Ce qui soulève la question suivante : la copie est-elle unique ? Nous répondons négativement en présentant trois copies différentes