# Talk:L(R)

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Field: Foundations, logic, and set theory

I added a dispute tag so that no one is accidentally misled by the page (as I briefly was). Statements that depend on large cardinal hypotheses cannot be described as "facts". The page should be rewritten to make clear which statements depend on large cardinal hypotheses, and which that don't. I would do it, but I'm not familiar enough with the material. -- Walt Pohl 15:41, 28 September 2005 (UTC)

I've added the dependency on large cardinals to the section header. Hopefully that should take care of it. --Trovatore 17:20, 28 September 2005 (UTC)

## Incomplete thought

I found the following passage, which contains an incomplete sentence, and removed it for now:

The purpose of L(R) is to study properties of sets that are constructible without recourse to the axiom of choice. Most properties of

I'm not sure I agree that that's the "purpose" of L(R). It's true that sets in L(R) have a certain definability property and that AC fails in L(R) (given large cardinals, of course). But I see it more as the smallest natural model of AD. I am curious to know what was coming after "most properties of...". --Trovatore 19:43, 28 September 2005 (UTC)

## Projective sets

Is it really necessary to assume large cardinals to show that projective sets are in L(R)? I would have thought it immediate. Ben Standeven 22:24, 27 June 2006 (UTC)

No, of course it's not oops, that could be misread--I mean "of course, it's not necessary". Yes, it is immediate. What I wanted to present in that section is what L(R) really looks like; originally I had the section titled just "Facts about L(R)", and mentioned in the text that the existence of large cardinals was assumed. Someone objected to that. I don't see any good reason to separate out what does and doesn't depend on large cardinals; the point is that there's a unitary coherent picture of what L(R) looks like, but you need large cardinals to prove some of it. --Trovatore 23:39, 27 June 2006 (UTC)

## Definition of R

Does it matter what exactly R is in terms of sets before we throw it into the machinery? When it comes to algebraic properties and ordering properties it really doesen't matter wether the reals is a bag of bunches of bananas or something else. Any two sets of reals composed of whatever are (uniquely) isomorphic when it comes to the usual properties. But say that we have some sanity requirements, like that any real must be an element of the von Neumann universe V. Can we take any $R \subset V$ passing as a set of reals and then proceed? YohanN7 (talk) 15:10, 24 May 2012 (UTC)