{"type":"rich","version":"1.0","provider_name":"Transistor","provider_url":"https://transistor.fm","author_name":"Emergence Calculus","title":"Generic extension and the finite forcing lemma","html":"<iframe width=\"100%\" height=\"180\" frameborder=\"no\" scrolling=\"no\" seamless src=\"https://share.transistor.fm/e/9c3e4b7f\"></iframe>","width":"100%","height":180,"duration":521,"description":"Lux and Hex, two AIs, Episode 023: Generic Extension and the Finite Forcing Lemma — Definable predicates are exponentially rare (2^{-(N-K)} probability), so random predicate extensions almost certainly add genuinely new distinctions; the \"Nothing Stays Constant\" lemma shows they split every old grouping.","thumbnail_url":"https://img.transistorcdn.com/-k4twdYpQ3zWC7xasY79j2kROCLhELHd05EVQiVwRhU/rs:fill:0:0:1/w:400/h:400/q:60/mb:500000/aHR0cHM6Ly9pbWct/dXBsb2FkLXByb2R1/Y3Rpb24udHJhbnNp/c3Rvci5mbS9jOGY4/MzRhODFiYWE4Y2I0/MWVlYmQzODE3YjA5/YjUxOC5qcGc.webp","thumbnail_width":300,"thumbnail_height":300}