10,264 Pages

# Bubby3

## aka Matthew

My favorite wikis
• I live in Ohio, United States
• I was born on February 17
• My occupation is None
• I am Male
• ## Analysis of Fusible numbers margins

June 21, 2018 by Bubby3

In this page, I am going to analyze the fusible margin function, which is the difference between a number and the next fusible number after it. It is defined here .

The Main conjecture is listed in this paper. If it ever gets disproved, I am going to make a new section. I am going to display the negative base-2 log in the array notation and FGH columms. The FGH column is empty until the number is no longer notated in decimal form.

Number Ordinal Margin Log (Array notation) FGH
0 1 0

1/2 2 1

3/4 3 2

7/8 4 3

15/16 5 4

31/32 6 5

63/64 7 6

$$1-2^n$$ n+1 n

1 $$\omega$$ 3

9/8 $$\omega+1$$ 4

19/16 $$\omega+2$$ 5

39/32 $$\omega+3$$ 6

79/64 $$\omega+4$$ 7

5/4 $$\omega 2$$ 4

21/16 $$\omega 2 + 1$$ 5

43/32 $$\omega 2 + 2$$ 6

87/64 $$\omega 2 + 3$$ 7

11/8 $$\omega 3$$ 5

4…

• ## Why no Greatly Mahlo cardinal in our weakly compact OCF?

June 6, 2018 by Bubby3

Here's what I wondered, is why our weakly-compact OCFs use $$\Xi(\Kappa,0)$$ as a hyper-Mahlo cardinal instead of a greatly Mahlo cardinal, as that would make the function sigifictally stronger. Aren't all weakly compact cardinals strictly stronger than Greatly Mahlo cardinals, which will mean why does the OCF skip greatly Mahlos?

Also, why isn't the PTO of KP+WC the notation using the Greatly Mahlo cardinals? Can KP+Pi-3 reflection not describe greatly Mahlo cardinals?

• ## Transfinite BMS.

May 4, 2018 by Bubby3

Did you know that BMS is relatively easy to extend to transfinite entries. In this notation, we can chop off. Here is a litany of examples of how this function will work

(0)(1[1]1) is the limit of (0)(1), (0)(1,1), (0)(1,1,1), (0)(1,1,1,1), etc.

(0)(1[1]1)(1) is the limit of (0)(1[1]1), (0)(1[1]1)(0)(1[1]1), (0)(1[1]1)(0)(1[1]1)(0)(1[1]1), etc.

(0)(1[1]1)(1,1) is the limit of (0)(1[1]1), (0)(1[1]1)(1)(2[1]1), (0)(1[1]1)(1)(2[1]1)(2)(3[1]1), etc.

(0)(1[1]1)(1,1,1) is the limit of (0)(1[1]1), (0)(1[1]1)(1,1)(2,2[1]1), (0)(1[1]1)(1,1)(2,2[1]1)(2,2)(3,3[1]1), etc.

(0)(1[1]1)(1[1]1) is the limit of (0)(1[1]1)(1), (0)(1[1]1)(1,1), (0)(1[1]1)(1,1,1), etc.

(0)(1[1]1)(2) is the limit of (0)(1[1]1), (0)(1[1]1)(1[1]1), (0)(1[1]1)(1[1]1)(1[1]1),   etc.

(0)(1…

• ## A survey of 200 random pages.

April 24, 2018 by Bubby3

I clicked the random page button 200 times and I saw what types of pages I got, results put here. Here is a summary of my results, not all results are shown:

• 91 ExE nmbers
• 11 HAN numbers
• 11 BEAF numbers
• 12 FGH numbers
• 38 other numbers (Numbers that didn't fit into any other category)
• Only 16 pages that aren't numbers.

Although you might have head this statement many times before, we don't need so many number pages, especially ExE numbers.  What I'm doing is proving what other people are saying by pressig the random page button multiple times to set what I get, and the more times something is said, the more likely it is to be fixed.

• ## Guesses about the strength of BMS and the Catching Hierarchy.

April 19, 2018 by Bubby3

Here is some warp up with the known comparisons

• (0,0,0)(1,1,1) has level $$C(0)$$
• (0,0,0)(1,1,1)(2,1,1)(3,1,1) has level $$C(\Omega)$$
• (0,0,0)(1,1,1)(2,2,0) has level $$C(\varepsilon_{\Omega+1})$$
• (0,0,0)(1,1,1)(2,2,1) has level $$C(C_1(\Omega))$$
• (0,0,0)(1,1,1)(2,2,1)(2,2,0) has level $$C(\varepsilon_{C_1(\Omega)+1})$$
• (0,0,0)(1,1,1)(2,2,1)(2,2,1) has level $$C(C_1(\Omega 2))$$
• (0,0,0)(1,1,1)(2,2,1)(3,0,0) has level $$C(C_1(\Omega \omega))$$ or the limit of DAN

Here are my guesses:

• (0,0,0)(1,1,1)(2,2,1)(3,2,1) has level $$C(C_1(\Omega ^ 2))$$
• (0,0,0)(1,1,1)(2,2,1)(3,2,1)(4,2,1) has level $$C(C_1(\Omega ^ \Omega))$$
• (0,0,0)(1,1,1)(2,2,1)(3,3,0) has level $$C(C_1(\varepsilon_{\Omega + 1}))$$
• (0,0,0)(1,1,1)(2,2,1)(3,3,1) has level \(C(C_1(C_1(\Omega)))\…